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Wi-sun = wireless smart Ubiquitous Networks.try this video for a brief overview.

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No consequence found, try original key phrase!ATLANTA, Oct. 1, 2018 /PRNewswire/ -- Landis+Gyr (SWISS: LAND.SW) introduced its aid for the Wi-solar FAN Certification software launched by means of the Wi-sun Alliance previous these days. As a Promoter Member of ...

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### 1200-year-old problem 'easy' | killexams.com real questions and Pass4sure dumps

CompactificationThe first problem I observe with this view is that the definitions are not well defined. consider 1/0=inf. Then inf=(1/0)*(-1/-1)=(1*-1)/(0*-1)=-1/0=-inf.A similar string of equalities gives 'nullity' being equal to both inf and -inf.

Zav"Imagine you're landing on an aeroplane"Landing ON an aeroplane? which Part of the aeroplane should I land on?

HiI like how he never really proves anything. every lone he says is "0/0=nullity." Okay? What's wrong with saying NAN? "Well," he would say, "Nulity is actually a number." Well that's great, but why cant you add it,subtract it, multiply it, divide it, consequence exponents, or consequence roots with it? Why does it mess of everything they already know about math? If the only dissimilarity between this "nullity" and NaN is that "nullity" is cnsidered a number, then I beget an idea. Why not stutter "aN" for "A Number."

Dangercrowx divided by x is always 1, so why would 0 over 0 live any different, it should live 1

IanFirst of all, if you are so opposed with the definition of a number nullity=0/0, why consequence most beget no problem with the definition i^2=-1?? there is no dissimilarity in the fact that they are both definitions of a non-real numberMost of the comments here too reserve using the 1=2 fallacy. This fallacy uses the assumption that 0/0=1, which is not upright in transreal arithmetic. In transreal arithmetic, you would net the result nullity*1=nullity*2, which is true.Also, the limiting process is not valuable here, because it only looks at values nearby to the number in question, they could define the actual number as nullity without losing the concept of limits.Nullity is different from NaN, for the simple intuition that, while NaN does not compare to itself, nullity is equal to itself. Every time.Even if they beget no exhaust for it now, who says they will never discover one???

DazliaHow consequence they solve an unsolvable math problem? do a original number and stutter it's the answer!!!

Pharme791Very nice site!

Joe"nullity - which sits outside the conventional number line (stretching from negative infinity, through zero, to positive infinity)"Nothing over Nothing = Everything? This doesn't do any sense to me...

PXwhat he is saying doesn't do sense. it's better to stutter that x/0 is infinity, since any number would meet in it. Assuming 0/0 is that nullity thing, does 0 times nullity equal 0? clarify that on his number line. How approach when you graph x/0, and you behold at the 0 point, the line is really at infinity? He obviously thought that he could just consequence what people did with square rooting negative numbers, which he can't, since the square root of negative one actually does exist, just not in the real number system. dividing something by zero isn't impossible, you just can't consequence it. Imagine you beget a trillion apples. You want to divide them evenly between zero people. How many does each person get? theres no people to give the apples too. It's not like every person gets nullity, there's just no one to give anything to.

Rajiv AmlaniTeaching kids a pile of rubbish. Shouldn't live teaching mathematics if you contemplate 'nullity' solves a 1200 year problem. Clown.

ChrisHe claims that 0/0 is nullity, a lone number with a obvious (albeit not strictly real) value, yet they know every real and complicated number solves 0/0=x, so it is not a lone number, it is undefined, it really is that simple. What he is saying is simply incorrect. too 1/x as x tends to 0 does mind to infinity, but 1/0 (and indeed a/0 where a is not equal to 0) is not equal to infinity, it is indeterminate, which is to stutter there is no value which solves 1/0=x. Infinity is not a number it is the concept "as big as they want", for 1/0 "as big as they want" is still not big enough.

me1=2

shoopofthedayit's basically the concept of imaginary numbers, except those are actually useful sometimes.

very ingenious oneHey! i just create a way, how can EVERYONE multiply two numbers just in a sec or two! Let's say, that every number which is greater than multiplied by ANY number is equals to BIGGETY. I hope i helped every lone the mathematic and Big number problems, maybe solved the spaceship problems as well.

Kenneth WongThis would defeat calculus. On a limit, the undefined is usually really important. To my understanding. Im still in middle school.

KazemiI. Hate. Him. That guy is a cheat. He just says 'Oh, hey, this here is a original attribute I "made" whose sole purpose is to divide by zero!' A lot of suited that does us.

achthe "we exhaust 0/0 in calculus" dispute is stupid. people, they consequence not net the value of 0/0 in calculus. they net its limit. there's a difference.

Bernard AzakieBritish schoolchildren "stupid"Have a nullity doesn't change anything. Your system will spit out "nullity" upon crash, but won't actually change anything. Whether something crashes gently or not is just a matter of crash handling.

DavidEXPANDING FAILLLL YUSHIN WASHIO.x*(y/x) = y if x and y are INTERGERS not equal.If you expand using zero, it will clearly give zero.Division by zero is NOT feasible using the RNS. nor is finding the SQRT of -1.

Sam O'Nouny"Nullity" is utter bupkis. It's just another course of saying "Not a Number", "Undefined", "Indeterminate", and of course, "Error". One cannot divide or live divided by zero. After all: 0/0=X; 0=X*0; therefore, X=All real Numbers, causing it to live undefined. Or is it +inf and -inf? *shrugs*PS-Rearrange "Sam O'Nouny" and you net "Anonymous".

Yushin WashioSimilar to the imaginary unit, it would live more useful to define 1/0 rather than 0/0 becuase anything is 0 if you multiply it with 0. So, 0*1=0, 0*0=0, 256*0=0 and even i*0=0. So, 0*(1/0)=0. However, since always x*(y/x)=y, 0*(2/0) must live =2, 0*(3/0)=3 and 0*(i/0)=i should every lone live right. Therefore, if 0^-1 is not simple enough for you, you can define your "nullity" as:0*1*nullity=1but 0*nullity=0and 0*-1*nullity=-1However, since the nullity itself without 0 is not defined, 1*nullity or -1*nullity remain undefined.

raymondlangley@tiscali.co.ukgreat news, now recommend me how can i net my ten year antique to learn divisions .. he knows his time table in head from 1/15 times but he just cannot understand divisions no matter how hard i try ...help please...

Siyang ChenThis is neither original nor useful. Computers already beget the equivalent of a 'nullity' (NaN) in every reasonable floating point data type. Moreover, this does not betray anything about dividing by zero that they did not already know (meaning, that the operation cannot bear any meaningful result with other arithmetic operations). Hooray for relabling an antique concept and claiming credit for it. Maybe I'll fade discover gravity tomorrow.

DanniThis is bullshit and he SHOULD know better. If he'd asked any one in the mathematics community he'd beget known he wasn't solving a problem because there was no problem to start with!He hasn't even checked to observe every lone the contradiction his theory presents.There are tons of ways to toil around the problem, the projective line being a very practical example. AND they those ways are more theoretically sound and non-contradictory. I won't bother to clarify it because obviously no one is interested in hearing real mathematicians talk. It's not like they just spent their terminal five years intensely studying it or anything. Never mind us.

MorpheusTake the blue pill, Mr Anderson.

Disagree1*0=2*0divide both by zero (which is an immposability)and you beget 1=2this number CAN'T live realand even if it was zero is the concept of nothing...infinity would live everything and so cancel it out not "nullity"

PaulThis is ridiculous. Dividing by zero is not a "problem," it's a mathematical impossibility. Inventing a title for an entity that doesn't exist doesn't occasions that entity to exist.Look at it this way. You recommend me there's no animal made out of cheese. I stutter yes there is, it's called a froopsie. And then I write, like, twelve papers based on the actuality of the froopsie and how I've solved the cheese-animal problem. The froopsie still doesn't exist, and I haven't solved the problem.Not only is Dr Anderson displaying a basic want of understanding concerning why this "problem" can't live solved, but he's passing it on to those destitute schoolchildren. Maths education is snide enough already. This man should live stripped of his teaching licence.

YanThis total view is utterly pointless. This man is just making up a original word for NaN, or undifined. And if someone can approach up with a practical exhaust for this, I won't belive it.

MarkThis original number has profound effects on the computing industry, by allowing the division of zero by zero many errors that beget previously made things impossible beget become quite possible.

Aaron J. Lang (phantom.penguin@hotmail.co.uk)I'm currently studying maths at GCSE but am one of if not the top in my year. The equations he does on the birthright are hard to read in the video but I beget a problem with the "definitions" he puts up on left, he simply states them, no explanation or deriving or anything. If anybody knows where I can find this then please recommend be, if not then his theory is just too unsupported to live taken seriously. P.S. I sure the greek epistle "phi" that hes using for "nullity" is already assigned to (((5^0.5)+1)/2). if its not and im being really blonde please contact me (address above), i really would like to understand this.

Tayler WamplerOK well I contemplate this guy is quack. If you *can* divide by zero, then wouldn't everything in Math live a lie? And pretty much, this is so useless. Who's ever gonnahave to divide by zero? People beget been doing Math how we're doing it now for.....I waver to stutter forever.....but a *very* long time. What's this guy trying to do, anyway? Create a revolution? Not gonna happen.

sarahi thought zero plus zero = zero. i too thought zero divided by zero was zero???

Scrapdogx * 0 = 4 solve for x.

GarashI always knew that such a number existed, if you pick out your Ti-83 plus, on the lifelike section, you write 1/x, you can observe in the lifelike that a nomber that would delineate 1/0 would live every lone the number, wicht is imposible in a fonction...

freddyIts not such a Big deal. I live substantive c'mon so there is a original number that noone is going to exhaust anyway. Woop-de-de,How many times are you going to divide something in real life by 0 anyway. It is just one of those pointless questions they stick on an exam.

ConfusedI todally consequence not net it. I live substantive how in the world can 0/0=infinity? It is just unpretentious cofusing! I guese that it might do more sense when ever I net taught it, but untill then I guese that I will just beget to live confused. Ta, Ta for now!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

kalebThis is stupid. It 'solves' nothing. It still, basically, says that X/0=NaN. It's a useless concept. Perhaps it will uphold computors, but it changes nothing mathimatically.

that guyi just divided my pacemaker by 0, but i havent died yet

a lofty school physics studentanother thing... phi is already a attribute for flux... nothing new

a lofty school calculus studentcalculus - where they divide, add, subtract, and multiply by zero and infinity fade net real answers every lone the time...

nikko holti contemplate this guy needs to fade back to the drawing board. i don't observe why they let him train this to kids like you always stutter do complicated things simple he's making things course more complicated.

ron jonesone divided is technically ifinity

Hmm...Fantastic! Extra stuff to learn at school!

MozeyThis guy basically deliver some sounds together, drew some lines and got a word and a mark for undefined. yoopdeedoo. The improbable Part is he confused one of the first things i learned in elementry math, you cant divide live zero. This just messes up the course i think. It goes against 'the essence of mathmatics is to do complicated things simple. Not do simple things complicated.' It just doesn't toil Mr.Frazier.

Alexis PeneffKind off It would befuddle me at first. But after a while i would net it. The theory is a bit strange. It will pick even more years to net the calculators and computers to beget nullity. I dont contemplate that my math information couldn't live divided by zero. It would pick my brain a lot longer to net this know then if someone created it when i first started math. My brain is already used to the antique style way. Other judicious i contemplate it is a suited theory. Though i beget never tried to divide by zero.

Sameera. KI am doing a physics coursework in which i am investiagtign whether how the thickness of the wire affects the resistance. However on one of my graphs, which is one over thickness, my teache rhas asked me whether or not the graph has to fade through the origin. But I create out that one over zero equals infinity, thereofore how can that live represented on a graph? However if thinking logically is there is zero thickness then there will beget to live zero resistance. This is why I ma quite confused.

Azathoth0/0 = X 0 = X * 0 So zero times what equals zero. Thats birthright boys and girls. Every lone number that exists. ... This is why it comes up undefined. DUH... If they want to approach up with a attribute that represents any number, fade for it. But its kinda pointless. 0/0 = anynumber, it equals 1, and 2, and 50 and 100 and 5000, and 2^58, and 281! and sqrt(1.52x10^235409) and 0 and i and -i... etc etc... consequence you net it yet? No DEFINATE answer. the respond is a variable that covers every lone possibilities.

LOLWhat the hell? Making up another number is not solving things -_-

aloofphila distinguished number of the below comments point out the various flaws in dr. anderson's idea. the value in it (if any) is that in mathematics you can define any constituent you want, as long as you are consistent with the accepted axioms and conventions. from a mathematical standpoint dr. anderson is just being silly, from an educational standpoint he's teaching his students a bit about how the mathematics progresses and how it has become the bailiwick it is today. unfortunately, he’s not consistent with that which has approach before him.

adammany people are forgetting, or simply haven't worked with higher math, but in calculus classes they very often toil with problems that would occasions division by zero. In many of the problems its as simple as changing some of the variable to more integratable or differentiable variables and derivating or integrating... pick a calculus class before relating conjecture that you know, obviously, very cramped about. Oh, and P.S. the solutions to many of these problems varies with each circumstance and the equations chosen, so, e.q. 0/0 could equal 1 or infinity or a set number.

The Anonymous RhoI contemplate everyone is delving too deep in the operation of division. Division, in its simplest form, is repeated subtraction (by its very definition). So, 20/5 is 4 because they can subtract 5 four times from 20 until they hit zero. So, let us examine 1/2. This equals one-half because they can subtract 2 one-half times and net zero. Great. Now, 0/1 is zero because they necessity to subtract 1 zero times from zero to obtain zero. Fabulous. What about 1/0? How many times must they subtract zero from 1 to obtain zero? Oops! That can't happen. That's why 1/0 is undefined. What about 0/0? How many times can they subtract zero from zero to obtain zero? Well, this seems indefinite. Could live 1, 2, or 1x10^2001. So, 0^0 is too undefined. Dr. Anderson makes conventions for the sake of making conventions; they can define 4/2=infinity. That's a convention. Let's not mention the fact that Dr. Andersen uses the laws of exponents for his lousy dispute or that the laws of exponents only toil for real numbers, so his arithmetic does not toil with his original number 'nullity'.

PoochyOkay, so he basically gave x/0 a original name, and completely against the sense of 0/0 (see l'Hospital's Rule). I fail to observe how this is revolutionary, unless re-naming stuff and making it convoluted is revolutionary. If that's revolutionary, I'd like to broadcast a revolutionary concept of my own: Plard. It's a constant that's between 0.5 and 0.6, approximately 0.573. Now gimme a Nobel Prize for my revolutionary concept. Also, the computer science aspect already has a perfectly suited solution - the try-catch statement.

BenSo essentially he just took the word "undefined" and gave it a attribute that he's calling nullity? I'm sure there's more to it than that, but that's what it looks like to me. Just trying to give computers a course to understand "undefined."

markI contemplate Dr. Anderson just proved the existance of god....

Peabnuts123I know the exact type of person this guy is; they every lone do. He's that guy who is always trying too hard to live positive, to listen to everyone's ideas, and to think, to actually BELIEVE they are correct. My deputy principal is just like this guy. I can observe this guy sitting in his office, or wherever, talking to his buddies saying "i don't observe why everyone thinks this total 'divide by zero' thing is so hard. Why not just create a original number to account for it? It's really quite simple". Thinking about the theory itself, like someone mentioned previously, dividing 6 apples by 2 give 2 groups. Thus dividing by 0 gives 0 groups. Also, when multiplying the previously exampled two groups by two, you net the original six. If you beget divided something into nothing, then multiplying backwards by any amount, will still give nothing. Thus proving anything(besides 0)/0=0.

JoeLook, here's how it is. x^1=x, right? And to net x^0, you divide x^1 by x. They already know that x^1=x, so they can stutter that x/x=x^0. This is the obvious part. Now, if they do x = 0, then we're saying that 0/0=0^0, or written differently 0^0=0/0. Dr Anderson is saying that 0^0=nullity. He already said that nullity is just 0/0. So basically he just proved that 0/0=0/0. Which is great.

Joe WhiteheadI was sure that was not the only one to contemplate of 'innumeracy' constants! It's chilly to observe someone finally find a exhaust for them. The problem is that the division isn't reversible. ;) The fact that one infinity may not live the very as another is another issue every lone together.

Math fanTo Kevin: It is not 1 divided zero times. It is 1 divided into 0 groups. When you beget 1 divided by 2, you are not dividing 1 two times. That would create 3 groups. You are making 2 groups. So the problem arises when you try to do 0 groups. Also, there is the principle that 0 divided by anything is 0. In the case of 0/0, it contradicts the principle that anything divided by itself equals 1.

creepxthis is just ridiculous! there's no consistent course of defining a division by zero as a number. you will only finish up in inconsistency.

AlyssaNO! you can't divide by zero. it's impossible. i will yell if you can divide by zero. no lie. it will prove that every lone thing in math was a lie. i loathe math.

Okinaptz UglwfSo "nullity" is "outside the conventional nubmer line". In other words, nullity, as x/0, is not defined "inside the conventional number line". Big deal, really ...

Some guyDivision by 0 is not possible. Just behold at the graph of 1/x. As x approaches 0, f(x) approaches +/- infinity. For this reason, anything divided by 0 cannot live 0, as somebody else said. Plus... If x/0 is defined, then you can prove that 1=2.

AdamHaving encountered Dr Anderson at university, I beget a more specific comment. He could consequence with marking some students toil instead of spending his time naming undefined numbers. Here's my original number - it's called 'the answer'. Give me any problem - the solution is my original number. In conclusion, Dr Anderson is a computer scientist and not a mathematician - there is a world of difference.

pr0pr0the problem i beget with this, is its not really math, they are inventing a number to fill in a missing piece of a puzzle, which is *far* from complicated math. dividing by zero does not give anyone any ANY useful mathematical numbers OR formulas, it is the very if the result is "nullity", which would really live no different then an mistake message: it still serves no purpose to mathematics as a whole. spending your life calculating pi and trying to find an finish is more useful then "nullity" (mainly because it would reserve Dr James Anderson diligent so they wouldn't beget to endure more of this kindergarten math... summary: if you could just invent a number to solve a thousand year antique math problem A. its takes away every lone legitimacy of said problem B. Roman mathamaticians could beget easily thought of it: if it was a suited view (which it isnt)

JohnWhat about this? 0 = 1 / &#8734; 0 = 0/1 0/1 = 1/&#8734; (Cross multiply) 0*&#8734; = 1*1 The sum of eternal 0’s still amounts to 0 so: 0 = 1. Isn't this the very line of thinking?

PhredFor those interested in understanding the topic of zero, I recommend Charles Seife's book, "Zero: The Biography of a risky Idea." Of particular interest is the first appendix, which uses the 0=1 proof to note that Winston Churchill is a carrot.

Aaron2 divided zero times is not two. Dividing it zero times gives you zero parts of a sum. Imagine dividinig 2 a half a time if you can. You net 4. Dividing two a quarter of a time gives you 8. pick this infinitely nearby to zero and your respond approaches infinity, not 2.

Senor BSThis is utter BS. 0/0 is the exact opposite of "Nullity". It's defined as some number which, when multiplied by zero, would equal to zero. This means that 0/0 is equal to every lone numbers, rather than none. BS.

MaxI contemplate Part of the problem arises due to the course zero (0) is used alternately to delineate void (nothing) or the infinitely minute 1/inf. Void isn't 1/inf, void (0) would live more appropriately linked to "Not a Number" (NAN). The infinitely minute still has size and eternal progressions never gain zero. It's always puzzled me how slack mathematicians are when considering stuff like this. Far from being rare probs like this crop up every lone the time in computing and programmers can't exhaust sloppy maths to toil around it. 1/0 would therefore live better represented as 1/(1/inf)=inf perhaps they could beget a original symbols such as Q to reprsent the infinitely minute and exhaust 0 to delineate nothing or "no number". Thus div by zero would live x/q=inf

MaxI contemplate Part of the problem arises due to the course zero (0) is used alternately to delineate void (nothing) or the infinitely minute 1/inf. Void isn't 1/inf, void (0) would live more appropriately linked to "Not a Number" (NAN). The infinitely minute still has size and eternal progressions never gain zero. It's always puzzled me how slack mathematicians are when considering stuff like this. Far from being rare probs like this crop up every lone the time in computing and programmers can't exhaust sloppy maths to toil around it. 1/0 would therefore live better represented as 1/(1/inf)=inf perhaps they could beget a original symbols such as Q to reprsent the infinitely minute and exhaust 0 to delineate nothing or "no number". Thus div by zero would live x/q=inf

KevinQuestion. What's so difficult about the thought that 0 divided 0 times is still 0? 1 divided zero times is 1? 2 divided zero times is 2? This is division right? That or if it's fractional the respond is always 0. Is that where this total bit comes in? -Kevin

josephi learned that myself when i was 8 thanks!

SocratesBah. This is ridiculous. Why not just stutter that 1/0 equals infinity and proceed from there? You know, like mathematicians consequence every lone THE TIME? The only problem that leaves is 0/0, and you only net that in places like eerie limits, in which case math has more than enough fancy tricks to fade around (like LaPlace's theorem). And that nullity attribute is just a capital phi. Not very inventive. Also, I would like to status for the record that anybody who can stutter "Imagine you're landing ON an aeroplane..." with a straight kisser should not live teaching anybody any sort of high-level math. Not to mention the fact that even Bush isn't dull enough to consider the possibilty of a pacemaker dividing by zero.

sylThe CS bailiwick already has a designated course of referring to what you net from dividing by zero - floating point has a defined NaN - NOT A NUMBER. You cant achieve any arithmetic on Not a Number. If you COULD achieve arithmetic on it, it would live picayune to "prove" that every lone numbers are equal to every lone other numbers - its a common mathematical brainteaser to give a chain of expressions that ends with " 1 = 0 ", with one of the steps being cleverly disguised division by 0. contemplate of it, you beget six apples, and you necessity to divide by two - you divide the apples into two groups (of three) Even on this simple explanation, if you were to divide by zero, you'd necessity to divide the apples into zero groups. It doesnt live substantive anything.

BertProfessor B. and Hmmm your both right. It is the lamest theory and in programming they consequence beget that exception handling to deal with problems that may occasions things to crash... I contemplate this guy just want to net into the word and live seen... So he will invent any solution to problem or theory that would give five minutes of fame. As for teaching school children with lame theory as this nullity is stupid.

Blueit just sounds like there giving something a title rather than just saying it's an unknown factor...

WinjaThe biggest evidence that this has no mathematical basis is that 0/0 is different from any other real number divided by 0. 0/0 is not undefined. It is indeterminate. As an undergraduate math student, I beget solved 0/0 in several problems. Sometimes it's undefined, sometimes it's 3, sometimes it's e, sometimes it's infinity...it can live anything. If I can understand this as an undergraduate student, I worry about how he received his doctorate.

2=1Wow...slow word day huh. This is absolutely absurd. This is similar to that silly 2=1 proof that gets whored around the net. Zeros cannot simply live cancelled out.

FaroukI contemplate this view is very interesting. Why? Because they necessity ideas to redefine the basics of their information to solve and cover more problems. Their goal is to solve more problems. When this view helped to solve some unsolved problems, then you may contemplate that this view may live the lone smart view of the century or even the millenium?! However, it is to soon to judge that :)

Poly EsterSo you create a attribute for undefined. You're soooo clever!

svThis is just pointless. Dr. Andersen is just making a dumb "new number" that will change many things for the worse. It will do programs harder to write because they now beget to know when nullilty will live used. Its a nice idea, but not thought though enough. Anyways, the onlypeople who will understand this without complaining are students who havent heard about this topic yet. For everyone else, it will befuddle you even more. i contemplate that this is the dumbest thing that ever happened to the world of mathematics. Its like changing the word mathematics to hahehahe. It confuses and makes no point. One more thing, what is that Part about "nullity", being in a original number line, that must beget been a cramped kids's thought.

Nicolas CapensI've read parts of Dr. Anderson's articles now, and my biggest gripe is that he doesn't really solve anything. Certainly not division by zero. He redefines 'undefined' to prove that the undefined of 0^0 is the very as the undefined of 0/0. I believe this is redress (at least in his algebra), but it doesn't really uphold us. Airplanes will still crash when dividing by zero without handling the exception. I submit a number Q^-1 that is defined as the number you beget to multiply 0 with to net 1 (just like the imaginary i is the number you beget to multiply by itself to net -1). Just like i solves the problem of working with the square root of negative numbers, in practical situations, Q^-1 solves the problem of working with the division by 0. Also, i is physically meaningless unless you multiply it with i to give -1, and Q^-1 is meaningless unless it's multiplied by 0 (which is equal to Q, Q^-1's reciproke) to give 1. The most valuable axioms: a = a*Q^0. a*Q^z / b*Q^w = (a/b)*Q^(z-w) {b !=0}, a*Q^(z-w-1) {b=0}. a*Q^z * b*Q^w = (a*b)*Q^(z*w). a*Q^z + b*Q^z = (a+b)*Q^z. Applying it to 0 / 0 gives 0*Q^-1. So that multiplication by 0 gives 0. Because Q is orthogonal to i they can actually define a three-dimensional space. For instance the square root of -1/0 would live (0+1*i)*Q^-0.5. 0^0 does not seem to live 0*Q^-1 though...

Edward CherlinNaN has been a feature of IEEE floating point arithmetic for 20 years. Before that, the non-values Bottom and Nil were used in Computer Science for every lone functions that didn't beget proper values. The real number line and complicated plane beget been extended for well over a century with an eternal value which makes them topologically complete, and Conway numbers can exploit arithmetic on infinitesimals of every lone orders. Alternatively a plane can live extended with a line at infinity, as in projective geometry, and every lone of the points at infinity can live represented in homogeneous coordinates using only finite numbers--the sort of thing your graphics card has to consequence to manage the obvious meeting point of parallel lines. Painters learned to do lines at infinity toil back in the Renaissance. You can behold every lone of this stuff up on Wikipedia. So this is picayune and not word at every lone to artists, hackers, or mathematicians.

Rick BurginI would've discovered this a long time ago if I'd beget realised I could create my own number outside the "conventional number line". It's like playing a game and making your own rules up as you fade along. What a failure.

DustinWhay cant they focus on curing cancer instead of making up numbers? Seems to me to live a better exhaust of their time.

Nicolas CapensCorrection to my previous post: Numbers can't live both a division of zero and a multiple of zero at the very time, so only one bit bailiwick suffices. I too beget a better notation: Lets write 5(/0) as 5*Q^-1 and 3(*0) as 3*Q^1. And define Q^0 as 1. So it's an algebraic remonstrate like the imaginary i. So in their binary representation they only beget to store the exponent of Q. real numbers beget a Q exponent 0. Divisions by zero beget an negative Q exponent. Multiples of zero beget a positive Q exponent. With just two bits they could prevent up to double division by zero exceptions. © 2006 Nicolas Capens

TurkutomI believe there is one exhaust for the term of nullity. Nullity equals Dr. Anderson's IQ divided by the product of Dr. Anderson's supporters. That being said, I correspond with the comments made by the majority of the responders. Nullity is merely a original word to stutter that it is either undefined or defined as itself.

Nicolas CapensThis approach has only (limited) exhaust in computer science. stutter they necessity to compute a * b, but an external library only gives us a / x. So they beget to multiply with b * x, but if x = 0 then they net NaN and not a * b. The solution is to reserve the numerator when dividing by zero, and set a bit that indicates division by zero. stutter a = 5 then they could write 5 / 0 = 5(/0). too when multiplying by zero they reserve the original value but set a bit that indicated multiplicatio by zero. stutter b = 3 then they could write 3 * 0 = 3(*0). When multiplying a and b they net 5(/0) * 3(*0) = 15. The (/0) and (*0) bits cancel each other. So basically 0 / 0 is still undefined, but (a / x) * (b * x) is defined as a * b. Obviously, this doesn't really solve anything, because the software should live able to compute a * b directly. A well designed external library has to provide a separately as well. It can effectively avoid division by zero crahes in badly written software though. But it still has its practical limits. If they beget (a / x / y) * (b * x * y) then they necessity extra bits to bespeak double division by zero and double multiplication by zero (four bits actually suffice for up to triple division and multiplication by zero). Even if they add those there would still live an exception and a potential crash when dividing by zero four times... © 2006 Nicolas Capens :-)

Jonesi contemplate that this is pointless

Professor B.This has to live the lone most lamest theory so far this millennium.

Hmm""Imagine you're landing on an aeroplane and the automatic pilot's working," he suggests. "If it divides by zero and the computer stops working - you're in Big trouble. If your heart pacemaker divides by zero, you're dead."" It's called exception handling...

jaclexWell, complicated numbers were not considered before but now they observe its application in the real world. So, let's find out if the theory about nullity can pass the mathematical community. Thus, how will they muster this original set of numbers (with nullity)?

Arnold SchmidtTo observe the failure of Western citizens to achieve any degree of basic mathematical literacy, behold no further than this idiotic piece of "journalism." "Dr." Anderson's "nullity" attribute is neither theory nor discovery; it is merely a publicity stunt by a hapless "professor" who realized that BBC reporters are, to deliver it mildly, dumb. This article is an embarassment to the mathematical community everywhere.

JKSit sounds like he's suggesting that dividing by zero leaves you with a value that represents the set of every lone numbers from -inf to +inf... IE: infinity. They already knew that dividing by zero left us (basically) with infinity. This is fairly stupid.

The judicious ManAn infinitely null view amounting to nothing.

JeffIt seems that people are very content to title something, thinking it will help. But it's just a convenient appliance that doesn't fade anywhere. Until I observe where it is useful, where this original attribute holds any more sense than 0/0, then I'm not convinced.

roy bobI heard that miscrosoft is running a original service pack to update their OS. - if they knew this theory a year before most of their security updates would do nosense. This is the desmonstration that they where right, their software is the best, but they couldn't manage what they don't know. every lone their programmers are older than 16, so they know nothing about nullity. Intell is now working with apple to solve the problem in future versions of their processor. - They are really apprehensive about implications: they are still evaluating how far consequence they beget to fade developing a original ALU for this. So we'll know much more in the future.

nullityThis is me, I got solved. btw, the problem is not this theory, solving an inexistent problem.. They allow a dull operation, divide 'nothing' into 'something'. I remember I was told to consequence NOT add 'pears' and 'apples' because "it can't live done". Lets fade further, avoid any mathematical theory regarding "0 divided by", just because it can't live done. For now lets title this brand original theory the "End Point theory". Whenever you find the "0 divided by" patter, stop, as it can't live done. mm better if fade one step further, Lets doubt the axioms of the actual theory: Instead of trying to solve the solution 0/x, consider the problem this kindly of situations, "if this course leads you to 0/x, then your course is wrong from the beginning", don't gyrate the solution a original problem. I'm the only one who thinks that maths where created and can too live changed? or they still must to thank god for this?

Dr Charles AllerstonThe length of this thread clearly proves that infinity exists.

AniketI contemplate 0/0=nullity="Nonsense!"

Uncle DaveI admire this. Using nullity I can now complete my design for a perpetual motion machine. Patent Office here I come!

PointlessNullity solves nothing. It's a original course to consequence the very thing- that is, nothing. Nullity still can't live manipulated into any profile of exhaust other than the uses other concepts beget fulfilled via calculus equations. He's just trying to do it seem like he invented something, when he just reworded it in essence. And shame on the BBC. I always thought they were smarter than to actually publish something like this.

seymore butswell if you had 2 apples and deliver them into 0 groups then there wouldnt live any apples because there is no group to deliver them into right? that simple...

Tomek PerlakRe: a physics proof --- But haven't you just proven that the first equation does not 'always' apply, hence a better one, including both the mass and the frequency should live applied? --- Please, note, this is said from a 'mere mortal' point of view --- and yet, what you've said could point to a conclusion that mass and frequency are not really two different concepts, but more so two different 'interfaces' to the energy in matter? --- Anyways, if there are two equation in exhaust for energy, I would too 'allow' for two different cases with 'nullity' in them; just a thought;

Jason DickThe dull thing about this is that mathematicians beget been dividing by zero for quite some time. It's basically a requirement to consequence any calculus. The concept of nullity adds exactly nothing whatsoever to mathematics: they already beget well-defined concepts for how to deal with division by zero. This is, essentially, the very as somebody declaring that he or she knows how to pick the square root of -2, calling it negativity or some such.

Interesting, but...Nothing from Nothing Leaves Nothing! Billy Preston 1974

EngineerThis is the most pointless BBC article since "Sudan Man ordered to Marry Goat". I feel terribly sorry for any of his pupils, that upon taking maths above GCSE will find that their genius of a teacher has in fact taught them total rubbish. And of course the fact that Transreal Computing Ltd requires publicity has nothing to consequence with this ridiculous claim.

Nikolas BourbakiI find the results very interesting, after having read the explanation on Wikipedia. please read further before going too crazy, he is working with "transreals", not the real number system. Perhaps it would live better if he too invented a original attribute for his trasreal zero, unless his zero is real, I'm not sure what the case is. Oh well, I contemplate I'll fade sharpen some pencils demurely and give my sliderule a wipedown before retiring to the library.

DanPerhaps this is a suited time for me to discuss my own recently published research. 1.9999... repeating is "pseudo2". In every respect it is like the number 2 except that the result of arithmetic operations using pseudo2 are decremented by 1 and added to 0.9999... repeating. This brings me to my next research topic called "pseudo1" which I am currently working on, but every lone I will stutter for now is that it requires a radically different pick on how they observe mathematics and could beget revolutionary benefits for computing. If you don't believe me I'd live pleased to note you working protoype applications demonstrating my research.

Christopher JoyceI'm confused? transreal arithmetic states that ln[-1]={PHI} where as complicated arithmetic states that ln[-1]=i{PI}; so while transreal arithmetic considers ln[-1] to live nullity (and not complex), complicated arithmetic considers ln[-1] to live complicated (and not nullity), so aren't transreal and complicated arithmetic inconsistent?

Joe BarkunI didn't really understand the real exhaust for this "new" theory... And could you please exhaust it in a ratiocinative MATHMATICAL equation or application...

tutti"sits outside the conventional number line"... in other words, it isn't a number? That's cute.

Mikei don't observe what the distinguished point is though, it needs purpose. dividing nothing into no equal groups (aka 0/0) i don't contemplate will consequence us any good. with the want of value divided by the want of value your not getting anything substantial and to any power except maybe the zeroeth power it remains the same. If there will live a exhaust for it i really hope i net to observe it. And no uses are stated although it says it has use. "Make every lone kinds of sums possible"

Darrenyou consequence realize that if this is upright then 2 now equals 1. observe this proof: assume a=b so starting: 1.a=b 2.aa=ab 3.aa-bb=ab-bb 4.(a-b)(a+b)=b(a-b) 5.a+b=b 6.2b=b 7.2=1 the only thing keeping this from being upright is step 4 to step 5... division by (a-b). since a=b then a-b=0, and division by zero making the proof false. he just made 1=2... yeah beget fun with math now... when 1+1={1,1.5,2,3,4}

AimeeNullity seems no better to me than undefined... what's it equal to? How consequence you exhaust it in sums? Where does it meet on the number line? Does it necessity a different axis, like i? I necessity a suited definition, then I'll contemplate about it.

Karl BabbittWhy not accept that YOU CAN'T DEVIDE BY 0!? Nullity is a very snide idea, looks like a caveman came up with the symbol.

Rainer Raisch, Munich, Germanymultiplying with zero always gives the result zero. Its not reversible like infinity as result of the division x/0. This "problem" needs no cure.

bdIt's clear that this had to approach from a computer "scientist". Any secone-year math student would pick it apart within seconds. I just phenomenon how BBC fell for that nonsense, I thought higher of them.

DevildogTo live a suited theory, a scientific theory must among others live apposite to real-world problem solving. Other from that, I must stutter it's an reverence to beget Mr. Norris remark on this page. Thank you.

JonAxioms 19 and 20 are troubling (bijectivity of reciprocal and 1/0 = infinity). Doesn't sit well with calculus.

Arturo MartinezDr. Anderson: Axiom 16 (NULL=Inf*0) is not at axiom at all, check: NULL=-NULL -> A9 1*(0/0)=-NULL -> Definition of Nullity 0*(1/0)=-NULL -> A13 0*INF=-NULL -> Definition of Infinity in R^t 0*INF=NULL -> A9 I'm still not sure if R^t can build a consistent algebra

Richard R.This is perhaps the stupidest thing I've ever heard. I am led to believe that neither Anderson nor the journalist of this article possess a mathematics proficiency higher than these students who are being lied to.

Braindead DanWell, shouldn't 0^0 = 1? Because 0 divides into itself once, like any number divided by itself 1^1 = 1, 2^2 = 1, etc... Just my thoughts.

Jorian HooverI contemplate I've got it. This "nullity" is prety much the very as undefined, but easier to express on paper. I phenomenon how rapid this will spread around. -Jorian Hoover

Zach M.Being a senior in lofty school, I observe this and think, "Well, I won't beget to worry about this." Then I realize I'm about to head into college. Well, now that I've heard of the concept, at least I can mentally prepare myself for it. And if this keeps up, I'll just beget to reserve myself mentally prepared when they rush out of epistle variables and start using animals.

Bob BinkmanI find it quite captivating how Pythagoras got to toil on a 1200-year antique problem more than 2000 years ago. :)

Vader PietIf you guys like real math about infinity, please read the book: "The Mystery of the Aleph: Mathematics, the Kabbalah, and the Human Mind" or just search for Georg Cantor and why he spent his terminal hours in a mental institute.

Victor*LOL* I contemplate people should live less ireful at Mr Andersen and direct their mock at BBC for running such a hilarious article. Bravo BBC, you're competing with the tabloids for the trait of reporting. Any birth calculus student knows that the concept of a restrict resolved the division by zero problem ages ago. The fact that computer returns an mistake does not live substantive there is a problem - it simply means that it is incompetent to exhaust the computer output without thinking about the round-off issues and the like. Millions of professionals exhaust existing algebra to cipher anything from portfolio allocations to space shuttle trajectories, and I can assure you that any future Mars expedition won't miss its orbit for the want of nullity in its computer system.

Caoltan Strainstupid. doesn't prove anything/ do anything any better. its still, in reality, undefined

Jimmy JohnsAccording to Jakes theorem, when Nullity is plugged into the quadratic formula, they find that Nullity is obviously equal to (1-C). Therefore, (1-c)^2-(1-c)+C = 0; And in consequence C=0. Thus proving that nullity equals (1-c), or 1.

Sara PostmaYou are my hero!!! i admire you!!!!!!

WoxorThis might live useful for pedagogical purposes, since it's often uncomfortable for students to learn that some things simply "don't exist" (like 1/0), but it has very cramped scientific value. Computer programs still can't divide by zero, but they toil around that by handling those sorts of exceptions. This is just another course of handling the exception, so to speak. From a simple math standpoint, I'm apprehensive it's completely useless since the addition of nullity to the reals would reserve it from being a field, or even a ring (0/0 * 0/1 = 0/0, but a*0 =0 for every lone a in a ring), so multiplication would fail. And without multiplication, there's no necessity for 0/0 because it requires the concept of division. From a topological standpoint, it's already been done, since 1/0 is treated as infinity in many ways when constructing complicated conformal maps, for example. It's too a bit crude to assume that this has even been a problem, that it has been a problem for 1200 years, and that some guy just came along and solved it with the mathematical equivalent of rewording the problem. It seems the best quantitative description of the worth of this hypothetical discovery is nullity itself.

Gregory C.Maybe Dr. Anderson's brain tried to divide by zero.

David NI suppose everything would live just fine if your pacemaker tells you that your next hearbeat should live in nullity milliseconds instead. This theory is neither revolutionary nor useful. No-one should live taught mathematics by someone who marks plus and minus infinity with dots on the real number line.

Nurse DragonbreathI believe Ray Lashley (way down the list) comes closest to the solution of this mystery. BBC is "pulling their legs". They wave this 'Crazy Doctor' with his flawed math in front of us in order to provoke reactions. And they fade straight into the trap! I'm not sure it was BBC, but I'm sure it was some Brittish channel which, a few years ago, aired a kindly of 'game show' having people who slept on the streets as participants. The contesters were made to accomplish various humiliating tasks like trying to build shelters from cardbord boxes and other junk. Those who did not win (in what appeared to live a very unfairly judged contest) had to fade back to the streets with next to nothing. This provoked an outrage from viewers who phoned and wrote to the TV station saying 'you can't consequence this to people' etc. Actually, it was every lone a scam, aimed exactly at provoking this kindly of reaction. It felt suited then to observe that people reacted against the 'game show', and (since I pot this is a similar case) it's suited now to observe that people really care so deeply about math. And by the way; I contemplate I solved these math issues terminal night, if you just care to read on. What they want is a definition of the restrict 1/x as x approaches zero (currently math defines this value as NOT limited, but rather as 'growing without bounds' iow NOT existing, iow indeterminate. But I beget the solution! let x and y live arbitrary postive reals, so that y

Mathew PeetZero divided by Zero should live a number on the number line. It has to equivocate somewhere between minus infinity and infinity, (including 0). For approximate values of 0 perhaps there are solutions. For real 0 the respond has to equivocate everywhere. It would live more useful to contemplate of the respond as 0 +/- infinity. Or indeterminate. Thanks for this sage it was useful mental exercise :)

papersnowmanI correspond with Rob. Debating and deciding whether or not this theory is an valuable task, but more importantly, why is a theory that hasn't been fully proven/reviewed being taught to their children? If this theory proves to live wrong, would you like to know that your children will never understand higher even mathematics because they had this theory inbedded into them at such a immature age? Also, at these ages, children pick information like this as simple 100% undeniable fact without much secondguessing at all, by the time this is proven one course or the other for sure, it will live ingrained in their heads too deeply to remove, for most of them. -- Papersnowman

BobAnyone who has even just completed basic programming knows about "null" and thus this is not a breakthrough.

MichaelThis is weird. This is not dividing by zero, it's just like saying 0/0=x. X could live anything. I'm a sixth grader in the US, and this is just unpretentious stupid, even though I don't understand the comments above I can observe that they point to nullity being inconsistent. Setting a variable for 0/0 is hypothetical to live revolutionary? I contemplate not!

ericwow. this journalist should learn more about a topic before reporting on it. he/she acted like dividing by zero could actually work. "nullity" wouldn't toil because its not consistent

Nick>>"Right or wrong, it always surprises me how many people are willing to live pretty nasty to someone who's approach up with a different course of thinking. Why is it so personal to people? Why consequence people insist the other person is stupid?" The intuition it angers people is because Dr. Anderson didn't even try to prove the consistency of his number system, let lonesome net it published in a reputable math journal. He just contacted the press to net his 15 minutes of fame. This is very frustrating for people trying to consequence real mathematics, who beget published extensive articles on why this makes no sense and yet net no attention whatsoever from common people. Now mathematicians laugh at him (and rightfully so), which just reinforces the layman viewpoint that science is a Big collusion that rejects criticism and alternative theories. Yes, mathematicians are perfectly birthright to live ireful and to pick it personally. If he wants to live taken seriously, he should publish a paper on it before teaching it to a bunch of grade schoolers.

MatthewWrong, his "solution" is like saying: one can net to the other side of the universe by going faster than the speen of light. It's nice to say, but doesn't live substantive anything at all.

A. CummingsI'd like to point out that 1 divided by 0 is not infinity. Dividing by 0 is actually an illogical expression because 0 doesn't beget a value. For a division expression to live mathematically ratiocinative the denominator needs to beget a value.

GiorgosIf professor can clarify to us every lone what is the original number then yes he solved the problem. Until then the only contemplate he proved is than the 0 in the power of 0 equals with 0 divided by zero.

endloserSo... if I am looking at this right... zero is nothing... it is already just a belt holder. You really can't multiply by zero because you had nothing to start with. Just like you can't divide, because you had nothing to start with. If you assume that one of nothing is nothing, then no parts of something is nothing. There I divided by zero. Not infinite. Just not existant. Maybe the respond isn't dividing by zero but getting rid of the belt holder and embracing the nothingness. And how to delineate nothing? With nothing. Just a thought... one that got me detention in grade school for being "insubordinate".

AySz88One of the *first* things he does on that whiteboard is wrong: 1/0 is not and should not live defined as infinity. It can live either infinity or negative infinity. Graphing f(x) = 1/x makes this obvious, or you can try this: consider 1/x. Let x live a positive number, and shrink it towards zero. This is like approaching x=0 on the aforementioned graph from the birthright side. The result grows towards infinity. Now let x live a *negative* number. Now 1/x approaches *negative* infinity! 1/0 can live considered either infinity or negative infinity, depending on what the math is being applied to.

l.schatzHe is introducing a original constituent and he doesn't even define a original set. He uses multiplication of the antique set without prooving he can exhaust it. I phenomenon if he proove the possiblity to interpose this constituent or if he just exhaust it without thinking of consequences at all? destitute pupils if he train such theories without prooving them!

Oxford Mathematics MScJeremy Lundy, it is not discordant to beget nullity = e^(-nullity) in this model. pick for instance the fact that a*infinity = infinity when a is a real number. This does not prove infinity is discordant when infinity is defined in the course by Anderson here. too contemplate about a*0 = 0. I very much doubt whether nullity is going to live of any use, but the mathematics doesn't seem to live discordant to me.

BradMany of the education majors I went to college with were in Remedial Math. Apparently some of these beget developed their own mathematical style. But if giving a particular kindly of indeterminism a title proves to live a useful pedagogical crutch, why not?

DoctorbDr. Anderson saying that 0/0 is a number is like saying that an egg is a number. Would he like to define what he means by a number?

Pennywise the ClownTwo things: The theorem T81 [(a*b)^-1=a^-1*b^-1 : a=/=0 and b=/=neg] needs to live an axiom, because the axioms don't seem to justify the guarding clause. Plus, this means that before, division by zero was not allowed, now with division by x*0, x negative, I can't exhaust T81. What's the Big gain? It seems this only complicates things.

ED?As a 2nd year maths student I was very excited to hear about the possibility of dividing by zero. But it turns out that is not what's happening at all. Now I am disapointed, but my heart warmed to observe so many people pointing out every lone the flaws so I don't beget to.

Andy L.Since Dr.Anderson will live answering questions later today, here's my first question. 1) Given that the even Gentzen's system for his consistency proof for Peano Arithmetic is itself not been proven consistent, how can you live sure that the Essex Dr.'s mechanical proof of the consistency of your system is anything but hotair?

Matthew HareRight or wrong, it always surprises me how many people are willing to live pretty nasty to someone who's approach up with a different course of thinking. Why is it so personal to people? Why consequence people insist the other person is stupid? He's either birthright or wrong, or he's birthright in a unavoidable field, and wrong in another field. But consequence people actually necessity to net personal about it? Who are they? Are they distinguished minds? Or consequence they just contemplate they are distinguished minds?

AndrewWhat's wrong with creating a original concept of Nullity? It may uphold out like "i" did (imaginary numbers, sqrt(-1), etc.) in the understanding of previously unsolvable concepts.

GeorgeI really contemplate that this original theory may actually uphold people and deliver alot of money, time, and even lives. too I beget seen alot of negative feedback from people just because they dont understand the view and they contemplate its preposterous. Open your minds. You should at least give Dr. Anderson a chance and remark on it later on.

Jeremy LundyUsing his defintion here is a proof that shows nullity isnt consistent: Assume to the contrary nullity is consitent. Let x=0^0 = nullity lnx = ln(0^0) lnx = 0*ln(0) lnx = 0*(-infinity) (since its a point live his definition) lnx = 0*(-1/0) lnx = (0/0)*-1 lnx = nullity * -1 x = e^(-nullity) Hence: nullity = e^(-nullity) This is a contradiction. Hence nullity isnt consistent.

AnonMSo, lim(x->1) (x-1)/lnx can live evaluated using L'Hopital's. It yeilds 1. Or, if you don't know L'hopital's, behold at a graphing calculator and find the restrict of the function as x->1. But, by direct substition in the restrict they net 0/0 (one of the indeterminate forms for L'Hopital's), so the restrict would live the nullity symbol- no necessity to apply L'Hopital's if they beget the "number" by direct substitution. As math should live consistent, apply the transitive property. They now beget that "nullity" = 1. Well, it equals 1 for THIS problem, they could, of course, do it equal any number of their choosing by changing the restrict problem (multiply the x in the numerator by your favorite number). Or, consider the structure of division related back to multiplication [6/2=3 because 2*3=6]. If they consequence this for 0/0 they beget the following: 0/0=? becomes 0*?=0. Any number could live filled into the question impress (which is why undefined is an preempt response to 0/0). Thus, if they are to beget a word or attribute for 0/0 or 0^0 [the very thing by exponent rules- which is why they beget a^0=1, if a==0] then "nullity" isn't a suited one. It should live "everythingy".

T. VukI correspond with Dr Noisewater.

cameronhow is calling 0/0 "nullity" any more useful than simply saying it is undefined?

CurtIndeed, he's too making the assumption that every lone infinities are equal.

Andy BI had him as a lecturer for computer graphics, and he explained this to us. I followed what he said and came to correspond with him that something divided by zero is not "on the number line". Big deal. Computer Science, and many programming languages, already exhaust NaN - Not A Number. Heck, I didn't contemplate Infinity was a number either - certainly, I can't delineate it as a binary number... Also, having just approach from a Control Theory lecture I was annoyed by the total 'number line' industry - every Cybernetics undergrad knows you can't really beget numbers without imaginary numbers - so it's every lone a plane anyway. ;op Still, some of the maltreat here is unwarranted - I thought he was one of the better Comp Sci lecturers, and clearly very bright. like some comments say, though, I did contemplate 'big deal', and he isn't a mathematician.

s squaredIf Dr. Anderson is reading these comments: I would like him to complicated on how his system differs from IEEE flaoting point standard's NaN, +infinity and -infinity.

X37VI don't really contemplate they can consequence anything with 'nullity' yet. It's just another name, really. But what is useful is the view of numbers off the number line. If they can device out more nubers like this, maybe they will finish up finding a total original number line, and find out how to actually exhaust 0/0. It's the concept, not the current usefullness, that's important.

Shanna WilcoxSo I can observe where he's coming from. Technically they consequence not know an exact value for infinity, but when you devide by infinity you net the approximate value of zero. Therefore I am birth to believe that if you devide by zero, "nullity" you would net the approximate value of infinity. That just makes sense to me...

Bill GoughVery captivating the even of enrage generated by a useful idea. They certainly know from family dinners how much insecurity (or its mirror image - smugness) determines a matching even of anger. I've read postings suggesting that a thinker live 'flogged' and others dismissing postings because of 'language' This original symbol, no matter what its application in math, is proving to live a fine generator of class-bias and racism. Hmmmm - might live something to this concept.

James LaniganI am an aerospace engineer and I correspond fully with his theory. You guys don't know the history of math. You just believe what the math community wants you to. I know the history of math. Now if Gene Simmons was teaching this, I would believe it.

LukeDr. Anderson wrote a reply waay down somewhere explaining that he has formally axiomatized trans-real arithmetic, and that it has been proved consistent. While it is facile to approach up with contradictions using Nullity and ordinary arithmetic, I am interested to observe his axioms. It may not live an incredible discovery, it may live an captivating system to toil in if it is consistent. please give details.

Dr. LimeyToo complicated to train the total world this original theory. They should ignore it.

ReidMost of the posts here are just stating the incorrectness of Dr. Anderson's work, but nonexistent of them give a truly rigorous proof of the inconsistencies. Due to Dr. Anderson's agreement to remark on the criticisms of his theory of 'nullity', I thought that I'd give such a proof for him to remark on. Hopefully, the BBC will retain the formatting of my post as it will probably live difficult to read without the necessary white-space. They start with some definitions. In the video provided by the BBC, Dr. Anderson gives the definition of infinity to live 1/0. In a post on this article, someone posted as Dr. Anderson (I will assume here that this is actually Dr. Anderson) and had this to stutter (he implies this in the video as well): "It is just an arithmetical fact that 1/0 is the biggest number there is." So, to deliver this in rigorous mathematical language, they beget the following from Dr. Anderson: 1) infinity = 1/0 2) infinity is an constituent of the real Numbers (hereafter denoted R) 3) R is bounded above by infinity They too know that R is a bailiwick and 1 is an constituent of R. To note that Dr. Anderson's proof is fallacious, they will note that one of his basis definitions (infinity) leads to a contradiction. Let infinity live defined as in 1), 2) and 3). It is too given that R is a bailiwick with 1 an constituent of R. From the axioms of a bailiwick they know that for every a and b in R, a + b is in R as well. Thus, infinity + 1 is in R. But, by the accustomed ordering of R, they have: infinity

Steve JayOnce upon a time they had no number zero, then the Moors showed the Romans the original number they'd invented, and reserve keeping break-evens got a lot easier. This is no more controversial than that, really.

Edgar MatiasThis problem was solved in the 1960s by Abraham Robinson, a Mathematician and Logician. Using mathematical logic, he proved that you could extend Calculus to included "infinities" and "infinitesimals". He called it Non-Standard Analysis (Google it/him for more info). Basically, he defined a set of numbers called Hyper-Real numbers, that included every lone real numbers + infinities + infinitesimals. Any upright statement using Hyper-Real numbers is too upright using real numbers, so long as the infinities and infinitesimals cancelled each other out in the final answer. So, instead of dividing by zero, you divide by an infinitesimal number. You consequence every lone of your equation manipulation this way, and as long as the final respond isn't eternal or infinitesimal, everything is fine. It's a shame more people don't know about this. Much of basic Calculus was originally invented using reasoning similar to Robinson's. His toil just legitimized those approaches, making them valid proofs.

LazzerIt is improbable that the real problem with infinities is not even discussed. The result of division by zero is not a simple number. Why? When you divide by zero you delete information. Precisely you delete the information what was divided. every lone numbers devided by zero result in infinity. The problems start applying equality to infinities. In almost every lone cases this is not correct, because infinity simply has no identity. One infinity in not the very like the next infinity. Undefined is not wrong, but it goes to far because you can still determine attributes from the infinity e.g. when the infinity result from dividing a number by zero the resulting infinity too has the nature of a number even if it is not finit. Try to approximate the division by zero dividing with numbers like 0.1, 0.01, 0.001, 0.0001 and so on. If you devide the numbers 1 and 2 this way, you notice the result growing. The equations are 1 / n and 2 / n. It is clear that (2 / n) / (1 / n) results in 2. But using infinity you cannot stutter 1 / 0 = infinity and 2 / n = infinity. But infinity / infinity must not result in 2 because it has less information than the source if the infinity. The quotient of such infinities must live a number, but you consequence not know which. Unknown numbers are represented by variables, normally. You too can delineate infinites by variables to distinquish them. Using phi for a number ist just a variable without a useful name. You're unable to reference that number. Maybe in some cases you consequence not necessity a reference. But you too beget no further capitalize for your calculations.

Brian FantanaSorry about my dangling friend's assorted rambling, but Dr Noisewater is very hard to reserve pacified these days.

S SquaredYou write that Dr. Anderson will respond questions about his theory of 'nullity' on Tuesday. If so, and he reads this comment, can he please fade into more detail about how his system differs from the IEEE floating point standard's NaN (Not a Number), +infinity and -infinity.

Dr Kenneth NoisewaterI would like to know why he didn't present this 'solution' to some lofty even Math students. Oh, but I already know the answer, because they actually understand complicated mathmatics. This doesn't solve anything programming wise, you might as well assume that 'nullity' is synonymous with 'error'. If you're dividing by zero in computing, you're generally doing something wrong. What exactly are computers hypothetical to consequence with 'nullity', and where are it's practical uses, other than another title for something that is undefined.

ChristopherOk first, one cannot define infinity = 1/0 because 1/0 is undefined (and dividing by zero is what he's here to define). What infinity can live defined as is: infinity = 1/n as n approaches zero But fine, they can pass that up. In his proof, he has: 0^0 = 0^(1-1) 0^0 = (0/1)^1 * (0/1)^(-1) 0^0 = (0/1)^1 * (1/0)^1 desist birthright there, he has an indeterminate form, 1/0 is undefined, this line in the proof has to live upright in order for the result to live true. But, he gets around this because he has defined 1/0 = infinity, which is every lone kinds of wrong.

FigsThis is why they beget try{} constructions. Why would 'nullity' live useful? I observe no intuition that nullity would live better than NaN.

BartBThere was a rumour that a U.S. status in law defined PI = 3.0 Such definition, fortunately, did not do it so.

TelanisThis is a silly idea. Computers cannot exploit "nullity" any more than they can exploit "N/A" for 0/0. mistake checking will not live replaced, it will simply live misnamed, and more errors will approach as a result.

SylvaniaI absolutely understand it. When will this live taught in schools around the world. It fills a big gap of understanding when studying Calc.

DarmokWhat? Is this satire? If so, it should live clearly indicated instead of presenting this as some sort of credible concept. And if not, is there no one at the BBC intimate with mathematics who can review these stories? Or at least contact an expert in the bailiwick or at least a local professor before publishing garbage like this. BBC, you should live ashamed.

jackhey, some of you people bother me. how many of you beget said "1/0 = infinity" here is why that is NOT true: 1 = 0&#8734; = (0+0)&#8734; = 0&#8734; + 0&#8734; = 1+1 = 2 see, it doesnt meet real math if 1 = 2 anyway, every lone that this guy is doing is making a attribute for this indeterminate result. instead of just writing "not real" or "indeterminite" he decides to do a cramped attribute for it. as far as i beget seen it has no implications beyond allowing computers to not freak out when one divides by zero

BlueRajaThis doesn't solve any problem related to Computer Science... Computers don't inherently know how to divide (or consequence anything, for that matter); they beget to live taught - someone has to design the circuit for division, and device out what to consequence in the case of divisor=0. In most cases, an exception is thrown or an mistake flag is set; however, I've never heard of a system shutting off when dividing by zero (and I *highly* doubt they'd program a pacemaker or autopilot to shut-off in that case).

SymphosisJason, the intuition 1 is the restrict is because its a definition; made up because it suited their purpose. dont contemplate your dispute is accurate, very for many other of you people. In any case, I am not sure Dr Anderson has actually given us anything they can actually implement.. but nice trying..

LizzI am cheerful that BBC wrote about this. I never knew this was a problem, but by reading about Dr. Anderson's theory I create the solution myself. And I am not going to betray it here :-) Dr. Anderson's theory is wrong. That much I can stutter for sure.

AhmedI am an engineer .. i didn't understand what did Dr James Anderson came up with but it's something improbable !!

Ole-RoaldIn computer programming they pick hand of dividing by zero as a sunder event in where chain of calculations. How this event will live taken, will live decided by programmer during analyzing the environment in which the calculation serie is doing. As I know, the birthright decition will live done if division by zero occur. Therefore there is no occasion to live apprehensive of something going wrong in autopilots in aircrafts, and in pacemakers.

JThere is nothing original here. What Dr. Anderson has done is to pick those operations, (in the reals or extended reals) which result in nonsense, (in the accustomed sense) and exhaust them to define nullity, (specifically those cases which are not handled by the extended reals). To summarize, they now beget a original word for undefined. P.S. What happened to the co-authors of Dr. Anderson's on this subject? (See the academic papers on the subject: Perspex Machine 8 & 9).

Ste Millington (Software engineer with simple MathsWhat is the point of a computer happily churning away calculations involving division by zero without any errors only to find that the results don't beget any meaning? I personally wouldn't like to live on a plane operating with Dr Andersons original arithmetic when because of some programming mistake a division by zero occurs and the navigation system carries on regardless - giving us a position of nullity by nullity! Dr Andersons axiomatisation of his original number system does appear to live consistent (given a cursory glance) however it's just unpretentious useless! The point is that in the real world if you are trying to divide something by zero you beget made a mistake and any well written computer program should exploit these errors effortlessly. In Dr Andersons original system they gain the skill to achieve division by any number upon any number, but at what cost? Well to start with they can no longer infer that because x + a = x + b then a = b. This is such an ingrained and natural notion that adopting the original number system would inevitably lead people to error. Though sickeningly grandiose in tone Dr Anderson's first paper does at first glance appear at least to live consistent within in its own bounds. Fine. His second paper on calculus exposes a clear want of mathematical training and is flawed in many places. I would live amazed if any peer reviewed journal would consider publishing either paper.

Matt PThis looks about as useful as complicated (or imaginary or non-real) numbers in that in conventional and most applications, it is entirely useless, a mathematical definition with profile and no subtance. (finishing year Calculus student)

Suspicious Cricket FanI am indeed very suspicious. It seems as if this total theory has been invented to someway apply some formula to the impending Australia 5 England 0 result in the Ashes Tests to provide a "mathematical" possibility of England retaining the Ashes despite sending out a second rate alien legion XI who play like crap.

Eric MillDr. Anderson should net in touch with Dr. Stephen Colbert, an equally renowned logician, whose concept of "truthiness" has been getting an improbable amount of press.

JenniferWe every lone know that it's impossible to divide by 0... but is it impossible to MULTIPLY by 0?

p@Sorry, but could somebody please insitute a national programme to train people spelling and grammar? I realise some of the posters are not aboriginal English speakers, but the majority of the rest necessity to beget something equivalent to national service to uphold them learn to communicate. Once that is done, perhaps they could try learning some mathematics and, in many case, computer science.

Patrick DEMICHELOne of the most splendid instance of the stupidity of the journalists. There are tons of real astonishing scientific breakthroughs that they never ear about because too hard to understand for the quasi totality of pseudo scientific journalisms they observe on televisions and web and hear on radios. This non-problem is very picayune to demonstrate to pupils 0.001^0.001=0.9931 0.0001^0.0001=0.999079 0.00001^0.00001=0.99988 0.000001^0.000001=0.999986 Even non mathematicians observe this converge to 1 : then 0^0=1 This is not because your computer does not toil due to poorly implement code that you should contemplate that there is no solution. Why necessity to create absurd attribute for 1? please Please journalisms of the world, the best thing you can consequence when you beget nothing to write or stutter it to shut up and pick vacations, don't pollute their medias. One thing I can recognize here is : they are qualified to converse about nullity , even eternal nullity :-) And to finish most processors know what to consequence to divide by 0 , but the programmers necessity to pay attention to this detail and deal an interrupt or the Nan or eternal number they will net if they divide by 0

TuomasJason's resoning is faulty, as (1/x)^(1/x^2) goes to infinity as x->oo even though it approaches 0^0. The point of 0^0 in a calculation is "how" one is reaching the limit. The "nullity" has been around in computer science, most math processors beget a special "number" NaN, which stands for Not a Number. The result of 0^0 is NaN, which this professor calls nullity. Nothing to observe here, amble along!

LukasI suppose this could open up original branches of hypothetical physics, but in practical application, it's pretty silly. still I suppose this is no worse then when 'i' was assigned the square root of negative one.

IanCan you define a word, by using that word in a definition?

TewAnd here I thought dividing by zero was infinity...

Jason0^0 is indeterminate, but if you pick (1/x)^(1/x) as x gets very big is essentially 0^0. However, this restrict is 1, not this "new number" nullity. It is called indeterminate for a intuition desist wasting these kids time!!

MikeLet's fade back to the progress of the rational numbers. Two theorems. 1) For any rational number z, they beget that 0*z=0. 2. For x,y,z rational numbers, they beget that x/y=z if and only if x=yz. Now suppose x/0=z for some rational number z. Then by the second theorem, they beget that x=0*z. So by the first theorem, they beget x=0 and their original equation x/0=z becomes 0/0=z. Now they beget by the second theorem again, that 0/0=z if and only if 0=0*z. But this equation holds for every lone rational numbers z, by the first theorem, so 0/0 could equal any rational number and thus is indeterminant. This is why division by zero is not allowed, unless, you insinuate those two theorems are incorrect and thus are questioning the total progress of the real number system.

KostasThis is ridiculous. It is a shame for BBC to even beget it in the news. This guy is not solving any problem because there is no problem. Even infinity is a matter of definition. You can give 0/0 any title you want, there is nothing magic or smart about it...

Kate Monday, MathnetThe view is neither novel nor 'outside the box' - this is something plenty of mathematically curious adolescents consequence upon learning calculus. The intuition no one has previously bothered publish it is because 16-year-old calc students generally grow up and, if they tarry in math, amble on to deeper and more significant areas of study.

DrewI contemplate it is perfectly ratiocinative and necessary. As a computer science person, the skill to consequence this is priceless. And using nullity makes perfect sense.

Annettai net where you're coming from, and if math is always equal and such, why isn't that possible????? so like if i got to understand it, yeah, im sure it would do sense and stuff, but birthright now im just a kid with no view about it, but it sounds interesting. im inspired that someone could find a mathmatical solution for that though! lol :)

The theory of calculus"But Dr Anderson has approach up with a theory that proposes a original number - 'nullity' - which sits outside the conventional number line (stretching from negative infinity, through zero, to positive infinity)." Well gee, maybe Dr. Anderson should finish his course in math before he begins teaching it. Let's observe him count from negative infinity to zero, to positive infinity. Or rather, devise a fashion of doing so.

WillWhile he has every birthright to create his own axiomatic system, if I recall correctly, the conventional system has an axiom that you cannot divide by zero.

Kevin RollinsOh boy, this is just setting these kids up for failure if they ever gain higher mathematics. Calculus deals a bit in indeterminates like 0/0. You necessity to recognize that it isn't the real answer.

MarieIsn't it kindly of silly to label a concept "revolutionary" when everyone's already thought of it, and simply discarded it because it's not anything new-- it's just that we've chosen not to toil under this set of rules? If you want to invent a original axiom system, whatever, fade consequence your own thing, but it's really goofy to assume that it replaces the accustomed system and makes that system inferior because "no one's ever thought of your concept before." Um, everyone's thought of it; they just pick to toil with the accustomed set of axioms because there's nothing in their toil that makes "NaN" a particularly captivating thing to toil with. I contemplate taking limits is a much more captivating view than just slapping a definition on something that can't live in the real number line. At least they can toil with limits and consequence tidy stuff with them in the axiom system we've already made so much progress in. Who wants to start over?

DoubtfulIn his introductory definitions he states that 1/0 = infinity. Then in his fourth step he is multiplying 0 or (0/1) by infinity or (1/0) [see definitions, positive infinity = 1/0] which would result in the respond being 0 or [0/1 x infinity = 0 not 0/0 or "nullity"].

Dr. Viktor I. PlanckensteinThere are some very captivating things about zero, and triviality. First, "The actuality of a picayune is Indeterminate". This is very valuable and facile to prove. It says that you cannot prove whether an remonstrate is really itself, or if it might in fact live an identical clone of itself. That this is strictly "indeterminate". This is too upright of numbers, etc. This is Harris's Theorem, and is perhaps the most valuable theorem in every lone of mathematics. I'm not sure if nullity is the very as a trivial, but it might be. I am not intimate with what this man is doing. Next, when are apples equal to oranges ? When you beget zero of them !! Yes - indeed - zero apples is identical to zero oranges. There is no dissimilarity !! Triviality is not a trashcan. There is a distinction between the picayune and the strictly nonexistent. If this man is teaching nonsense to schoolchildren then he should live flogged. But if he is investigating the view of triviality then I'd stutter he should net a medal. I contemplate that I'd necessity to observe his math first before making that call. Is an apple the very as an orange ? Yes, when you beget zero of each !!! An apple is an orange !!! I am not advocating division by zero, but there is certainly MUCH to live said regarding triviality ! Respectfully, Dr. Viktor I. Planckenstein

Nathan BixlerNo sin to him or anything, but I devised a course of doing this terminal year out of sheer boredom. THe fact that no one else has ever done this astonishes me. too in my case, I used an L (the pound sign) as 1/0, and did every lone my math from there. But seriously, its not that inventive.

silhouettedThis makes no sense! Why doesn't the station realize how many people beget a problem with this and let the professor know how wrong he is?!

Sheaif(x!=0){ z=y/x } Are my maths revolutionary?

mikeThe dimwittedness of most of these comments posted here is wonderful. The people who are trashing this article don't even seem to beget a rudimentary grasp of language, making your claims to beget any understanding of the language of math laughable. To those of you who posted comments like "the BBC should publish an replete apology," and name-calling like "marons," thank you, you've made my day.

OtaX/0 has to live infinity. Infinity not being accepted as a real number by mathematicians, neither number being acceptable, and any number greater than zero leading to any value less than infinity, it leaves no other choice, unless they want to create a number greater than infinity, heaven forbid. The question is reversing the formula where then 0*infinity is X, but of course zero multiplied by anything is zero, real number or not. Is it really that hard to accept the view that there's one fashion that's irreversable?

JesseActually, 1/0 can live regarded as infinity in extended real number system (consider, also, the Riemann sphere). Naturally, this does not excuse Dr. Anderson's theory from being totally useless -- as others beget pointed out, this is essentially a redefinition of NaN.

Taaviofc they can divide by zero. At least in theory.. short course into known (not so well known, seems)three dimensional numeric system: "first" dimension: real numbers - including (positive/negative) infinity and 0 (based on 1) "second" dimension: complicated numbers - includes real numbers. There they beget so called real axis and imaginary axis (constituents are 1 and i={square root of -1} ) *about those 2 dimension there are plenty of definitive works available for everyone "third" dimension: That seems exact belt for nullity (call it however you want to). any complicated number divided by zero belongs to third dimension, which includes both first and second dimension Constituents are 1, i and 0/0. It's an extension to complicated numbers 0/0 ~ a, where a is complicated number (so basically 0/0 is complicated level) however a*(0/0) does not equal (a*0)/0 = 0/0, because 0/0 is basis component, therefore |a| is "heigth" of 0/0. But projected to complicated even a*(0/0) DOES equal (a*0)/0 = 0/0 = 0 (real number) if a is negative, then a*(0/0) is located below complicated even if a is positive, then a*(0/0) is located above complicated level. about x/0: as most of as know - x/0 tends to live infinite. in upon described three dimensional numeric system x/0 equals (0/0) times infinity (infinity, as it is in "second" dimension) So x/0 is a "border" of "third" dimension (where x is complicated number) well, as english isn't my first language AND it's 3:30AM here atm, i apologise for any mistake i did (either linguistic or mathematical). necessity some sleep tho. If requested, i can clarify it a bit closer tomorrow.

nullitycrap, ive been discovered

a physics proofok this might fade over some peoples heads but hey..... In relativistic physicswe can define engery as E =(mass x c^2)/squareroot(1-speed^2/c^2) which if the precipitate = c and the mass =0 comes out as E= 0/0 which acording to this guy would live equal to nulity which acording to him is a number that does not exsist in the everyday number line. but the precipitate and mass of a photon are indeed c and 0. and a photon does beget an energy defined by E=h*frequency which is a real number. the point is 0/0 is simply undefined thus if E=0/0 by one equation it could still live defined by using a different equation. Im sure theres a mathematically allegate course of stutter this but basically as the OS guy pointed out 0/0 can beget any value. so to stutter it is a number that is not on the number line is most deffentally wrong and it is indeed scary that this has been made word worthy as a piece of mathematics. maybe its usefull for computing but its tot maths

icecreameaterAhh man I was just getting trigenometry. Now they beget to add an extra grade to study something that's not there.

A.R.Yngve, SwedenYears ago I wrote a science fiction novel, ALIEN BEACH, in which the solution of "1 divided by zero" heralded a distinguished scientific breakthrough of virtually transcendent proportions. I wasn't really grave about 1/0... and I never expected a solution to approach true, either. But once again verity proves stranger than fiction, eh? ;-)

Oliver, 17, IB Maths Higher even studentI laugh but I yell at the very time. You step outside of the classroom and *wham*, you observe how dull the majority of your country is. Shame on the BBC, they beget just given me the only excuse I necessity not to pay my licence fee and switch to intelligence-powered media such as slashdot and b3ta. Oh Lord, "Could your maths information live divided by zero"? It wil consequence no such thing you hacks, but you beget just proved that bbc.allknowledge = 0

The GodfatherThe italians beget known forever that nothing divided by nothing equals nothing! A Big tubby ZERO! What is wrong with people! SHEESH!

RobThe valuable question is: why is an unproven theory being taught to school kids? I don't contemplate much of this theory myself, but that isn't the point. Even if it was the best thing since sliced bread it should still live peer reviewed and then added to the national curriculum before pupils net to observe it.

MattHmm, this is very strange. I don't contemplate he is right. I guess you could net a attribute kindly of like i that signifies something that couldn't exist, but then much of differential calculus would live proved wrong or picayune if this were doable for n/0. It could toil for elementary math, but I contemplate it does not apply to advanced mathematics.

AnnaThank youy, this is truely interesting. It wil pick math to a total original level. One down poit: Many childern will loathe you for making their homework longer and a tad harder. The rest of the world thanks you.

MathematicianI contemplate it is not just ridicoulus, it is offensive, I can't believe that this kindly of people were teaching, I would like to know where did he study and check his title. Did he realize that were confusing some children?

TriHmm, sometimes I contemplate people how post such scathing remarks are not even mathematicians themselves, while I too disagree on the dispute at hand, it is not however birthright to attempt mathematics when some of you appear to beget no view what math is also. for one thing, the complicated number plane does not exist in the real number plane correct? The complicated plane only exists when written down, hence why its the imaginary number plane, I believe some of you would ahve effort thinking in more then 5,6, or even 7 spatial dimensions or thinking that unavoidable subspaces are purpendicular to themselves and to every other number out there...some of you who dont know this might want to learn some Linear Algebra at some point and maybe you will gain some understanding before you do comments. Though I dont find the problem to beget been solved by creating a original variable myself. It seems lacking anyhow in substance.

ShaquelHi im in yr5 they dont consequence that in my school they consequence fractions and shapes and that

AndrewThe moral of the story? journalists (arts graduates) should not live allowed near science stories.

Tony HendrixDoes he not realise that when programmers write code - especially for essential purposes like pace makers they will check if division by zero is occurring?

Asaf ReichGreat. So now a pseudomathematician can fade around proving he's practically a mathematical Messiah ("It's that easy!") by teaching it to tenth graders. Wonderful. I don't suppose this report could beget been sensible enough require a mathematician about this, nooo. That would beget been far too...logical. Unlike this theory.

Alexander PoindexterThe very view of putting something that is beyond the third dimension into the views and constraints of the third dimension is the very as telling a baboon that you are it's father/mother and that it should act more human: absolutely absurd. They are limited by the three dimensions. To gain beyond that requires a thinking that extends past the 10% of the brain that they use. The terminal time I checked, this mathematician doesn't appear to beget transcended their conventional course of thinking. And for him to shove that kindly of thinking onto lofty school students shows no humility to the other established and more well known mathematicians in the world... I don't even beget a degree in mathematics and I can observe through this belt of thought.

StarF68Personally I contemplate it's rather pointless. The article claims that not being able to divide by zero could occasions major problems, even fatalities, but here's the thing: How often does this happen? Personally I beget no idea, but my own guess would live that it happens extrmeley little, if at all. But beyond that, how can you just create a original number which will solve one problem, without creating a set of it's own problems? For example, what happens when you try to divide by nullity? And back to the total computer thing, even if it does encounter an error, would it just shut down? If you programmed it to toil with "nullity" (There's another problem, you'd beget to upgrade existing technology to even recognize this original "number") then what does the computer consequence with it, just stutter "Oh, alright, stirring on..." Why not just do it consequence that with the error? It every lone seems rather pointless to me, and even absurd to do something up to respond a question.

PeteHere's a thought. If I beget x sweets and want to partake them out to y people including me, each person gets x/y sweets each. But if I beget x sweets and want to partake them out to no-one, not even me (out to 0 people), what happens to the x sweets? consequence they collapse on themselves as they nullify their own existence? I contemplate not.

AlexGuys, I contemplate a lot of you are missing the point, the guy is a COMPUTER SCIENTIST, not a mathematician. He's approach up with an intuitive solution to a grave computer problem. Does it matter if it's the real for upright solution if it works? The respond is no.

Not a math person..I'll admit this thing has me confused. But then so did i when I learned about it in math class. The only thing I can stutter aboout this is antique Albert Einstine was too ridculled.... for E=MC2... least till they split the atom.

NeoWait, I can device this one out... Okay.. So, nullity is--*Matrix explodes*

The XI am really against this. Proposing to do a number not on the numberline is ridiculous

AaronWell, this problems hasn't gone un-challenged before, and this hypothetical solution leads me to stutter that this teacher should just stick to the syllabus. The understanding as i and my friend came to was that it was incomprehendable, and they came to the agreement that the solution to the problem is "possibility itself".

The absurdity makes me laugh ...Taken from Mr. Anderson's paper: "Having capital Phi equivocate off the number line blocks the counter-proofs from real analysis that attempt to note that 0/0 is undefined." So basically, you're saying since "nullity" lies in its own unique universe; thus, it can't live disproved by any known mathematics. Gee, I didn't realize I could consequence that. In that case, I better inform my math teachers that I deserve every lone A+'s, because every lone my answers (even the wrong ones) conform to this original mathematical universe I invented jsut today where my answers are always correct.

El francoThe solution is wrong, there are no infinity, you could always add 1.

DeborahIt"s wonderful!Dr. Anderson has shown the eternal and the negative eternal impact on zero and given it a original name. From now on those who consequence not understand the theory of nullity will forever live called nullidiots.My husband is the very first.

SolarisGuruThis just goes to show, if you net enough people to back you up on something... IT WORKS! Why? There just needs to live enough people out there to fade along with you, and then it doesn't matter what anyone else says. Doesn't math already beget enough crap involved?

EngineerYou scientists who are bashing this progress don't quite net it consequence you? It takes an computer engineer to observe the potential here. By creating a "magic" number that REPRESENTS division by zero, every lone sorts of foible tolerant computing can live performed that wasn't possible. He uses that instance in his statement, and I beget approach across fatal computing errors due to zero division many, many times. Instead of requiring programmers to ACCOUNT for zero division, they can develop computational engines that can deal with such an operation. reserve arguing about abstracts you math geeks...this is why I net paid course more than you...

AnonShame on you BBC next time you publicize something about math, do sure that YOU don't understand it

SarahWell this isn't quite as silly as you might contemplate from the article - he hasn't just assigned a attribute to x/0 (which as people beget rightly pointed out is no different from NaN etc) but is proposing a set of axioms for 'transreal arithmetic' in which 'nullity' can function as just another number. No of course nullity doesn't 'work' as a number on the real line, but on the proposed set of extended reals it would. The aeroplane/pacemaker thing, however, is obviously ridiculous.

Derek AndrewsThis does seem to live stirring up quite a hornets nest and it makes me phenomenon if the programmer who set this page up gave any thought to what happens if there is an eternal number of comments.

jhughsJust reading through the comments and it occurs to me that it's pretty chilly to observe so much zeal about mathematics. (Okay, I was going to try to live amusing by saying "...so much zeal about nothing.", but that would live a discredit to every lone of you.)

BRN-Test1234Nullity is awesome can't wait to observe this in software.

PaulI asked 'Dr Math' of mathforum.org (proper mathematicians) what they thought, a suited summary i think: "Hi, Thanks for writing to Dr. Math. I've actually been waiting for somebody to write in with this very question. No, Dr. Anderson isn't coming up with anything new. Yes, he's missed a few details. It's valuable to address what he has really done. He hasn't approach up with anything original on the 1/0 score. Defining 1/0 as infinity is actually fairly old. The original thing he has developed is defining 0^0 = nullity (and defining 0/0 = nullity). Note that I said "define". Although he claims that it is a consequence of 0/0 = nullity, this isn't true. Some background information: Under the criterion real number system (the one they are taught in school), there is no infinity, nullity doesn't exist, and they operate under the math they were taught in school. For some mathematical applications, particularly those involving limits, eternal sequences/series, and some applications in computer science/engineering, they exhaust what is known as the "extended" real number system. The extended real number system includes two quantities they muster "infinity" and "-infinity". They define these quantities so that: infinity > a, for any real number a -infinity

SteveI don't understand how this works as anything new. He gave a computer example, so thats what I'm going to toil with. "If your pacemaker divides by zero you're dead." It should either hurl an exception that can live handled by the software (and either terminate on its own; 'killing the person', or trying to recover), or it should live checked BEFORE dividing it. Now, assume the division returns a special number. How is that pacemaker going to exploit that? The very exact course it handles exceptions that net thrown, or an assertion BEFORE doing the division. Either terminate the application or try to recover. Now my biggest question is how exactly is it planned to delineate this in a course a computer can understand? Lets assume the number is 1 byte, just for simplicity (this can scale up to however lofty you want). 0x0 (0) and 0xFF (255) are every lone taken. How does he aim on representing nullity? every lone 8 bits are spoken for. In a 32 bit integer, 0x0 through 0xFFFFFFFF are every lone spoken for (be it signed or unsigned). How does he aim on having a different number approach out of 8, 16, 32, 64 etc bits, when every lone the bits are already used. The only course I can imagine is the very course it is handled now: Throwing off a special exception. You CANNOT just stutter "ok, 0x0 will now delineate nullity". That does not work. Then any math done where the result is 0x0 (what is 2/100?) will return "nullity".

Ari RabkinMy first impress was that this was slightly kooky, but the distinguished thing about science is, the actual paper is online, and is pretty facile to follow. I contemplate I understand what Anderson is doing, and it makes sense, although I'm not sure I'd muster it newsworthy. Numbers don't approach from God; they can define them. everyday arithmetic defines multiplication and division in unavoidable ways, and does not define the operation of dividing by zero. It's perfectly feasible to tweak definitions to define a nonstandard arithmetic. People beget been doing it for years, with complicated numbers being the most celebrated example. If you behold at Dr. Anderson's definitions, it is indeed upright that 1/0 = 2/0, but no contradiction arises: that statement just says Nullity = Nullity, and multiplying both sides by zero doesn't result in 1 = 2. It's much like the course that sqrt ( 1^2 ) = sqrt( (-1) ^2) does not imply 1 = -1. As a number of people beget pointed out, most computer systems already exhaust an arithmetic system with positive infinity,negative infinity, and a special attribute called NaN (not a number). What Dr. Anderson is saying is, "look, if they tweak the definitions a cramped bit, they can net NaN and the infinities to behave in a more consistent course and behold more like the real numbers". Hardly revolutionary, but I can observe it being useful in some computer programming contexts.

Peter John YannoneMathematics has its limits. It is a finite model that they exhaust to analize an eternal subject. In the real universe, integer values are unachievable; including zero. But integers are quite useful in science and engineering. Zero is better defined as an asperation toward nothingness: as one over infinity. This solves every problem I beget applied it to so far.

AnnI would like to know how mr. Anderson defines 0. seem like he has forgotten to consequence that in the first place.

BrianIts called the extended reals people: R union {plus or minus infinity}. You can toil out an arithmetic, but 0/0, infinity/infinity, and infinity - infinity are still undefined.

BlahThe nullify attribute is already used in mathmatics. It is the greek epistle Phi and is already equal to something.

BeccaI contemplate it's really chilly I admire Math and would admire there to live a original theory to live proved but I don't observe how zero divided by zero can equal infinity

George AylorNot so rapid you naysayers! It was 800 years after the Mayans had the concept of zero before the Europeans caught on. So give Dr. Anderson another 800 years to prove his theory.

MarcusI'm okay with this. Much of math is created, not "simply derived by logic from nature." (Much of it is simply derived, just not every lone of it.) Given the portions that are just constructs: necessities like irrational numbers, why not beget a null number that allows us to achieve *around* otherwise dead-end operations. Regardless of that, it gives their computers and computer chips an eschew method. This is a suited thing. They may very well observe benefits in their own lifetime.

Jaharashma AtmakandahahrWhy can´t they just correspond that x/0 = x, or perhaps x/0 = 0, instead of having something mathematical that isn´t allowed (division by zero) !!! Division by zero is truly a real bug in the mathematical system which still hasn´t been corrected!!!

AishaI don't contemplate it's feasible to divide by zero. If Pythagoras couldn't consequence it, who can?

CliveThe axioms in his paper are discordant (assuming that infty, -infty and Phi are distinct). 0^{-1}=infty and (-infty)^{-1}=0 quickly lead to infty=-infty (axioms [A20], [A21]) since Phi=infty-infty=infty+infty=infty [A11,A5] they beget equality of every lone three "numbers".

BoratIn my country they hunt mathematicians.

MA in Maths and Computer Science (Cantab)Many people here beget missed the point. If you fade to his web-page you can observe that he has developed an axiomatic system that is very similar to criterion mathematical axioms, but slightly different - in the vein of non-Euclidean geometry. He has added the quantities +infinity, -infinity and nullity - really just setting out in mathematical language the rules regarding +/-INF and NaN in the IEEE floating point standard. Unlike complicated numbers, you can actually consequence anything original with these original quantities (e.g. the equation 0x = 1 is still unsolvable, 0x = 0 still has infinitely many solutions - nonexistent of which are infinity or nullity). Teaching children how to intuition logically given a different set of axioms is, in my opionion, a suited thing. However, to train them that this is a gallant original world and a paradigm shift for computing woyuld live a downright lie!

Jimmy KlavocWhat annoys me about this article is the suggestion that it will solve problems in the real world realm. As far as computers are concerned depending on the language you're using you will either beget to check beforehand that you aren't dividing by zero or ensnare a DivideByZeroError or whatever the type throws. I don't observe how making up another imaginary number (just like i and j) helps solve anything practical at all. i and j beget been useful, this seems to beget no such potential. Seems like someone has lost their head up their own you-know-wheres to me.

Computer Science PhDComputer scientists are embarrassed by these deceptive claims. The BBC should publish an justification for its cry-wolf reporting instead of trying to spin this as some sort of positive yeast with provocative or inspirational worth. Dr. Anderson's 'theory' hasn't generated the sound 'debate' that BBC portrays, it's drawn virtually unanimous rebuke from the public.

DavidThis is truly ridiculous. The total coverage and "idea" is nonsense. I beget no view why this nonsense collection of sentences is being reported on. Anyone with mathematical information shouldn't even fade as far to muster it a theory or dispute - it's just sheer lunacy in the profile of a few sentences. Perhaps next week you should route your reporter onto the streets one evening to require the drunk public if they beget any more reportworthy ideas.

anonquirky people consequence beget the birthright to create their esoteric math systems, even if they wish to rename and refine NaN to feel like they've done something new. but to advertise this as any kindly of breakthrough is hubris; to pitch what is in essence a tautological solution as capable of doing something different than NaN in already error-catching pacemakers and autopilots is to sell snake oil; to train this math to year 10 students and imply that it could ever live a Part of everyday algebra is grossly irresponsible. 1=2; 1/0=2/0; nullity=nullity; q.e.d. ?? it doesn't even fill everyday equality. if you want to inspire kids to math, recommend them about pythagorean number cults and note them fermat's terminal theorem.

R.C. J. WeaselDr. Anderson's theory leads to some surprising conclusions, such as the view that either you can't consequence anything with this nullity, or 1 = 0.

The Cat Baron(N^0) - 1 = 0 therefore ((N^0) - 1) / ((N^0) - 1)= 0/0 = N^0 + 1 = 2? Sounds just as dull as what this "teacher" says he has approach up with...

misteranonimous1/0 is not infinity. 1/x as x tends towards 0 is infinity. therefore you beget based an dispute on a counterfeit premise. fade and try again!

Alix PaultreThis has been needed for centuries, but especially now in an age of obdurate computer minds that cannot fail in operation. Just as "i" represents the square of negative one in order to achieve complicated math, "nullity" will consequence the very for zero. Dr. Anderson is a genius.

Dr. Gary H. KramerInteresting. The "new" number is really a named mistake trap. I observe no evidence how "nullity" can live used beyond the mistake trap. Also, the position he placed the number is in the complicated domain, so I suppose he's just extended the number plane to another dimension!

ThormOkay.. So he has redefined NaN? Nonsense.

JoeBlowMoMoI'll recommend you the giveaway: most original theories are peer reviewed before being made public. When you instead rule to present your theory to a classroom replete of kids (who don't know any better anyway), it shows that just maybe you suspect the grown-ups won't believe you.

Dr Michael G Koch, SwedenThis is a truely underwhelming solution of a problem that is not. It has been hovering in the air for much more than 1200 years like a brick does not. Thus the best remark is, in fact, that of Albert Einstein (look it up!). Dr Anderson should now, indeed, concentrate on the 2500 year-old problem of negative infinullity which not even Confucius has solved. It was the following line of thinking: Gottlob Frege - Wilhelm Ostwald - Ernst Mach - Rudolf Carnap - Moritz Schlick - Otto Neurath - Reichenbach - v Mises - Ludwig Wittgenstein - Kurt Gödel - Bertrand Russell - Lee Whorf - Karl R Popper - Quine - Morris and modern semantics, i.e., the konventional mathematics and logics, 20th century positivism, the Vienna coterie and the neurophysiologically inspired modern critical semantics, which helped us to eschew from the antique fashioned idle-running of philosophical pseudo-thought into the pitfalls of language: Why is something and not instead nothing? (Heidegger), What is the sense of being? Which foot is ugliest: the repugnant one or the repugnant one missing an repugnant toe? (Old Vikings next morning in the Celebration Hall), Who is bigger, mrs Bigger or Mrs Bigger's baby? (The baby, 'cause it's a cramped Bigger)..., the "liar's paradox", "Achilles and the turtle" etc. So let us just exhaust a cramped advanced understanding of language: Null or zero was once introduced in India (primarily a tiny central point, then a thick one, then a cramped ring, later stretching out into a bigger coterie and, finally, into a 0, looking for an facile mode to impress an barren space: 1, 2, 3 etc ment that there was a unavoidable quantity of something (people, animals, objects or units of parameters - like m, sec, V, A, mg, km/sec, l or whatever) on a unavoidable belt in the decimal system and 0 ment that there was nothing. Now their language permits us a confusing want of exactness to stutter both "He stole nothing" and "He didn't steal (any thing)". The dissimilarity of these two meanings is detectable by asking: (1) Did he steal? 'Yes' What did he steal? 'Nothing'. (2) Did he steal? 'No.' They beget a negation floating around in the sentence and their someway 'unexact' grammar allows us to deliver it somewhere. That creates many pseudoquestions, which can bother us of merely grammatical reason: It rains? What rains?? The sky? The air? The clouds? The water? The weather? No - they beget just a rule saying that a sentence needs a subject/noun and a verb to live complete. They deliver a toltally barren 'it' into the sentence to fulfill that requirement. Should they allow their language (as it is in some other languages) to leta sentence live without a subject, they would stutter only 'Rains!' instead - and the problem wouldn't only vanish but live impossible to put. To divide with zero is nothing else than not to divide. Otherwise one should deliver people into prison for stealing nothing, though - due to the infinitely minute theft - only for some millisecond. The problem here pretended to live solved is not existing for educated people thinking with real exactitude. It is just a question of some sort of 'advanced enlightenment'. Q. e. d. Michael G Koch, MD (open for comments)

Hungry HippoI'm not sure which made me laugh most: the original 'theory' or some of the attempts on here to disprove it. I had no view they were blessed with so many mathematical geniuses visiting the BBC.

Anoopanullity is actually used by ancient indian mathematicians for dividing by zero.. they said it as syoonamanak.. i thik there should live more study about it

MichaelHis view of the restrict as x approaches 0 of (1/0) and -1/0) is nothing new. phobos puts the redress theory of infinity below. Infinity is not a number and nullity should not live treated as a number. Also, since math is defined for three dimensional space Where would nullity fit. It is definitely not a complicated number and would not live in any Mandelbrot or Julia set. Jeff the U.S. topic with a masters in math is not far off in his ideas. However, if you behold at the restrict of (1/0) and (-1/0) you cannot leave the abstract fashion of calculus and its definition of infinity. By your understanding then infinity is just another defined variable where basic algebraic concepts can live applied. This does do sense. However, what is infinity? If it is the largest number feasible then (1/0)=(2/0)= infinity. So how can you deal infinity as a variable?

John KillaryIs it not a bit odd that this wonderful discovery in maths has been made by a non-mathematician, verified by two other non-mathematicians and published in journal of the Society of Photo-Optical Engineers. Why is there no mathematician quoted who supports it? Why was it not submitted for peer-review to a reputable journal of mathematics? I wish one of the school children had deliver this question to Anderson: If 1 x 0 = 0 and 2 x 0 = 0 then 1 x 0 = 2 x 0 Divide both sides of the equation by 0. You are left with 1 = 2 Some mistake here I think.

Me > Dr AndersonAsking for the respond to 1/0 is like asking where exactly is the EU in Britain. Let's deliver this another way; 1/0 is asking the question what number multiplied by 0 is equal to 1. The answer: A slap round the back of the head, since any number multiplied by zero is zero... Unfortunately the bbc has asked a computer scientist with the IQ a yoke of points more than a stick of butter who's interested only in stroking his own ego by claiming to live smarter than newton etc. Maybe the beeb should check such stories with actual mathematicians before just running with it.

Patrick KillaryThe BBC should publish an replete apology. This feature is an insult to mathematicians. Would the BBC note Physicist claiming to beget made a remarkable discovery in Chemistry without checking with a Chemist? Of course not. Then why publicise a hypothetical Maths discovery by a Computer Scientist? Did Dr Anderson discuss his theory with a mathematician? Has he ever taken even an elementary course in Algebra at university level? His rubbish would live laughed at in any first year university class. I am a Maths graduate and there is so much wrong with this that it is frankly embarrassing to watch.

dubsthis is just idle journalism- i know nothing about the theory so was very interested in the article- had the BBC done even some basic verfication they would beget realised that it's every lone been done before as has been demonstratedb here- i don't anticipate them to live experst on every lone things mathematical but a few phone calls could beget stopped them wasting their time with this- v dissapointed that something like this could beget made it far as South Today- i live substantive if they aren't gonna verify facts im sure i could approach up with more newsworthy items...

Shadowkillerphobos, their dear professor defined them as real numbers and opposite of one another. By his definition, they are the very number. In reality, infinity is a concept and not a number and thus it is not topic to the laws of math.

Simonif 0 is in the exonend of 0 it is not defined..for every lone other numbers it is 1... or am i wrong? so the start of the "theory" is not right.. how can the finish be?

www.forum.arbuz.comthis solution solves nothing! Dr just 'invented' original termin, thats it, nothing special...

AndrewI beget just reviewed the paper in question and I must stutter it is a load of antique rubbish. In the few proofs he gives he uses his theory to prove his theory. This is like saying "I contemplate the earth is flat, therefore the earth has no curvature, therefore the earth is flat." As I said simple rubbish or a very unfunny joke.

TobiasHaha, that's kinda nonsense. I mean, it's a nice idea, but it doesn't uphold at all, I think. For such problems, you could exhaust L'Hospital, but just if you beget functions which result in 0/0. Nullity is not the solution for this problem, it's just a short course out, which doesn't help.

Jo MillerIt's fascinating to observe the vehement reactions here. I don't beget enough background in algebra to quickly understand his paper, but I consequence beget enough to observe that since this is outside the real numbers, everyday rules consequence not apply (sorry folks with your apples and pies). It may or may not live nonsense, or useless, but I don't beget enough information to stutter for sure. As for teaching it to a class of children, well, so long as they understand that it's outside the accustomed system, and they can't exhaust it in their day-to-day calculations, no harm is done. Perhaps it will excite a few that there are entire original sets of number-like systems out there. Learning about imaginary numbers (square root of -1) at a similar age stopped me going mad with tedium in maths classes and led me where I am today, with 2 maths degrees.

ManiacI correspond with Evlis. I mean: a) In limitical calculation, terms like "0 / 0" or "a / 0" must not live replaced by original symbols, since they can live solved anyway b) Just giving it a title doesn't live substantive a thing. It still is not a number, since (I'll muster the original attribute P): P = 0 / 0 = (0 + 0) / (0 + 0) = (0 / 0) + (0 / 0) = 2P that only makes sense if P = 0, which obviously is not fulfilled (in general). Of course, one should beget a deeper glance on this toil before judging it, but I don't even observe where it should go...

LUtter rubbish. They shouldn't live teaching this sort of thing in schools.

DavidA quote of Richard Feynman seems appropriate: Now that doesn't live substantive anything. Suppose it's "Wakalixes." That's the generic principle: "Wakalixes makes it go." There is no information coming in. The child doesn't learn anything; it's just a word.

NickHow is this even useful in anyway? does it even qualify as word - i know that not much happens in caversham but approach on! A computer scientist should know better!

Elvisjust inventig a original attribute is not worth mentioning. sorry. (if there are other theorems behind it, i missed them in this article)

phobosShadowkiller wrote: ___________________ So wait, let me observe if I understand here. Nullity = 0/0. As the professor showed us, 0=1+(-1). So 0/0 = (1+(-1))/0 = (1/0)+(-1/0) = Infinity + Negative Infinity. As everyone knows, anything minus itself equals 0. So this means Nullity = 0. consequence I win a prize? _____________________ Infinity + (-Infinity) are not the very number... u can not determine the subtraction's result.

Matt Milford"Dr James Anderson, from the University of Reading's computer science department, says his original theorem solves an extremely valuable problem - the problem of nothing." Correct, haven't solved anything. Infact, you've defined it, these numbers by there nature are not defined on a conventional number line. "If it divides by zero and the computer stops working" Absolute BALDERDASH, this may occasions a problem if the problem is not correctly handled by the program, which the majority of computer system implementations are capable of handling these days. By the looks of this article you do it behold like this would live a valid attribute to exhaust in an equation, which it clearly is not. You can check for an undefined respond from an equation but you cannot exhaust this in algebra elsewhere. For goodness sake, consequence NOT train this to year 10 pupils! Since when has this been Part of the curriculum? More than the fact that I reject to accept this, what practical application will this beget to them?

Enigma in NorwayDivide by zero? What a load of codswallop! Division by zero never has, and never will live either a problem or a mystery. An autopilot cannot divide. It kan fade bananas or switch off; but divide? Give me a break! Dr. Anderson would live better off using his energy on something worthwhile.

geitWTF!? pythogoras didn't worked?! I solve everything with A²+B²=C²! Even grades for wad reviewing.

Caboosewhat are you every lone on about? I'm the result when you divide by Zero!

David HeilmannIf you divide by zero, you beget done something wrong beforehand. It may do sense so exhaust 'NaN' (not a number) to ensnare the corresponding errors in a critical computer programme, but it does NOT do sense to cover up errors in mathematical reasoning by using just one more symbol, which would even do it necessary to alter other valuable mathematical rules (can you divide by that thing? If 1/NaN=2/NaN, ist then 1=2? In Short: unnecessary and destroying mathematical clarity.

TomHe has only deliver original problem on top of the antique one... nothing original about the that. He could just as easily defined that anything devided with zero is zero. Just as anything multiplide with zero is zero...

It´s every lone nonsense...It´s every lone nonsense because instead of dividing ridiculous numbers people should better approach together amd do different kindly of stuff. Math is artifical (and boring), not real !

Phoebe TunstallThis proposal is painfully stupid. He's applied a computing concept (the view of having a attribute for "Not A Number" when a calculation cannot bear a sensible result) to generic purpose arithmetic in a course which will befuddle students. Actually it's worse than useless, because at least calculations which return the respond "NaN" can't live both equated together (2/0=NaN doesn't equal 4/0=NaN, as NaN isn't a number and as such no such comparison can live made) whereas Nullity = Nullity in Anderson's system. Whilst he may beget been able to construct a consistent arithmetic system around Nullity, it's *not* the very arithmetic system employed in primary or secondary school maths (in the very course that non-Euclidean geometry is a completely different system to the Euclidean geometric system school pupils will live working with). The fact that he's not making clear just how radical the differences are between his number system and the commonly used one suggests he either has a very destitute understanding of maths or he intends to mislead students into following his crankery for the sake of self-aggrandisement.

Arne GHm! Suppose they beget one apple to divide between 3 persons in a classroom. Each will beget a third of an apple. Let one person leave the classrom. There will live two persons left to divide the apple between them, a half apple each. Let one more person leave the classroom. The remaining ONE person net the total (=1) apple. Let the terminal person leave the classroom, there will live no persons left in the classroom to observe the apple left there, which means 1/0=0. Would that live a mystery or a "problem" at all? So, does a "nullity" really solve a "problem", which is not there?

KibYahQuote from the paper: "the transreal logarithm of a negative number is defined to live nullity. In both cases the logarithm can live extended to give complicated solutions, though they consequence not delineate the transcomplex numbers here." Since this contradicts nearly anything related with complicated numbers, I would muster it questionable to exclude the explanation which will certainly lead to a contradiction, e.g. &#934;+&#934; = ln(-1)+ln(-1) = ln((-1)*(-1)) = ln(1) = 0

Trevor WoodThis is very, very silly. I don't know what Dr Anderson got his PhD in, but it wont beget been maths.

P45I just spent every lone morning working this out, my boss caught me and sacked me on the spot. Therefore 0/0=P45!

BortWhat??? I'm pretty sure there's no such number as 'nullity'. If there is a problem with autopilots and pacemakers dividing by 0, then they just necessity to live better programmed. Certainly dividing by 0 shouldn't live a problem for an autopilot if the programmer thought of this possibility.

unforgivenSo it's much easier to cipher with an eternal number instead of an undefinied...

KibYahLet nullity live defined &#934; = 42 and the total theory makes sense. 42 is the answer^^ You can too define &#934; = apple or &#934; = coconut &#934;=0/0 simply means that &#934; is the (or better: one) solution of the equation 0*&#934;=0 which is solved by anything, not only numbers. An exception is infinity, because 0*&#8734; is still not defined. You could redefine it, though and give it a name, stutter ... infinitillity &#982; or something, or you could too exhaust nullity for this, just as you like. You consequence not solve a problem by giving a title to the unknown solution. In fact, I consequence not observe any Problem in 0/0 since you still beget to watch out when dealing with 0 for instance 1!=2 |*&#934; &#934;!=2&#934; |*0 0!=2*0 ??????? muster it &#934; or what you like, it may do sense but is no real use, because the main problem is that the zero constituent of a bailiwick does never beget a multiplicative inverse, and this cannot live solved without touching the axioms of group theory.

Dr Tim SouthernDividing anything zero gives either minus or plus infinity as an respond and has been this ever since I went to school (too many years ago now. It is very facile to demonstrate this respond and it does not necessity to fade outside their current number range. It is therefore, an un-necessary complication to a system that works well as it is. The fact that computers return undefined as an respond to dividing anything by zero is a software problem not a mathematical problem that requires software writers to create the redress definition.

Steve King0/0 = nullity - fine, I beget no problem with that. However, to attempt to cipher 0^0 by converting it to 0^(1-1) is wrong, because 0^(-1) is undefined (infinite). Try 0^2 = 0^(4-2) and you will too net 0^2 = 0/0 = nullity, which is clearly wrong.

QASIM:) IF YOU JUST WANT TO stutter THAT 0/0 is nullity then kindly dont dissipate their time on the white board,because you started from something and landed back on the very thing. sorry for being harsh,but please sound more convincing next time and dont note it to children,so it to mathematicians.

x-suicideComenius University: first try to prove lim x->0 0/x and then I will live pleased :-)

SuperChefIf I beget a cake and two people, I divide the cake by 2, and they beget half each. If there is only one person, they net the total cake - I've divided by 1. But if there are no people, I don't divide by zero, I just don't prick the cake at all! Attempting to divide by zero is an mistake that can only chance in maths and computers, which is why your calculator gives you an mistake message.

DSTRThat is so stupid... Is this a joke? What about NaN (or Inf) in floating point operations and non-classical calculus based on numbers inftly big (or small)? Does anyone else contemplate not beeing able to divide by 0 is a problem?

Crazy SwedeNumbers outside the conventional numberline is not something novel. consider that the squareroot of -1 = i The problem with Dr Andersson soultuin is that it is an axiom and thus by definition cannot live proven.

jaimeastorga2000I just watched the first videos, and... honestly, I understand he has to fade unhurried for the kids, but I still contemplate its amusing I fade from 0^0 to 0/0 in one step (I was experimenting with this problem) where it took him like five. XD Now, to his credit, this is something like the imaginary numbers. You pick something that can't live done (getting the square root of -1), stutter its not Part of the real number line, and give it a name. Except, you know, you can actually consequence SOMETHING with imaginary numbers. They are USEFUL.

Jamie BrowningThis is a meaningless idea, which demonstrates want of basic understanding in advanced mathematics. The bbc is irresponsible for reporting it as significant. Did the reporter try asking any mathematicians for perspective?

Steve RolesThis is utter nonsense. Forcing a computer to toil around the fact that it can't divide by zero does not live substantive that it is now possible. In mathematics it is still NOT feasible to divide a number by zero.

Schau UnImplemented in Java ages ago. Where is the news?

JLOK, distinguished work. Now you beget saved thousands of lives and are expecting the Nobelprice?

JAKToday nullity is in the classrooms what next creationism?

John TitorVery, very stupid... In 20 years, nobody will even remember this hack.

CraneThat's totally moronic. You can't just fade "Oh look, let's create a original number defined as the respond to this centuries antique problem!", then "Wooh! I solved a centuries antique problem!" He's an attention seeking idiot.

The OS guy0/0 is every lone values, at once. This proves it: 0.x = 0.y ( = 0) (0.x)/0 = y 0/0 = y/x You can substitute any numbers into x and y that you want, so this means that 0/0 is any number. You can substitute irrational numbers even...and how about imaginary numbers? You see, it can live any number you possibly want it to be.

AnonymousI correspond with every lone of you that claims that this is crap. I read some posts claiming that you shouldn't judge original ideas to soon and that the square root of -1 used to live troublesome. Only, this is nothing like it. As mentioned before, NaN (Not a Number) has been used for quite a long time with much the very results. Hoever, what is really troublesome is the media attention that this gets. You can't just report anything without checking with someone who knows what they are talking about. You should at least live able to mention that there are critics before publishing something like this. A dismal event for the media community!

MathWhizThe mathematical aspect of this proposed proof is seriously flawed. Foremost, infinity does not equal 1/0. If you start off with a counterfeit hypothesis, everything that follows it can live proven true. That is a basic proof principal. That may clarify why the subsequent parts of the proof appear to do sense to some people. However, the proof is flawed throughout its entirety. Initially, the counterfeit assumption aforementioned lonesome disqualifies the proof. Even if you can overlook this, when examining other aspects of the proof one would notice that the proof itself contains divisions by zero. One can't assume that since they are attempting to prove that division by zero can live correctly expressed, that they are allowed to divide by zero in their derivation of the proof. If divisions by zero were already allowed, this problem would not exist in the first place. The other major flaw results when examing the broad spectrum of the proof. Dr. Anderson begins the proof with 0^0=0^(1-1) and eventually ends up arriving at the conclusion that 0^0=0/0, or the greek epistle phi as he denotes it in his proof. Any mathematician knows that 0^0=1, thus again they notice a flaw. I am unavoidable that 0/0 does not equal 1. I prize ingenuity and innovative thought, however the integrity of mathematics must live upheld. This proof is not acceptable.

That's 30 min I'm not getting back...I can hear the chorus in the background as I watch the video (a la Southpark)... James Anderson, dumb dumb dumb, dumb dumb dumb dumb dumb.... Isacc Newton, smart smart smart, smart smart smart smart smart...

ViperO07Wrong... Just wrong, its the most idiotic view I beget ever heard. Its just a attribute for saying NULL or not on the number line because it is impossible. Crack heads... every lone of them. The chalk board says 0/0= nullity, which is false, any kid knows 2/2 = 1 3/3 = 1 etc, so 0/0 = 1 the problem is when you net 4/0 in which case, nullity is still impossible, because its just saying anything divided by 0 = nullity... thus nullity =1 thus wrong.

AnonymousWow. If 0/0=nullity, then what is nullity/nullity? Are they gonna do up another title for that? This solves nothing.

Mikael PalmgrenBrilliant!

AndrewSo if x/0=nullity, then x/(y-z) tends to nullity as y tends to z. "Tends to nullity"? If numbers were to "tend to" something that isn't a number, then mathematics wouldn't live of much exhaust now, would it? The notion of the "conventional number line" extending to a point at which it is "outside the conventional number line" is ridiculous. There is a dissimilarity between solving a problem and rearranging it to do it somebody else's problem. So this is what you net when mathematics meets early 21st century attitudes to things, eh?

PaulThis is just an endless chain of incoherences. The worst thing, as a friend told me, is that this guy is introducing children to this kindly of "stuff", to stutter the least. This is what happens when non-mathematical people try to net into mathematics, they hardly beget an view of what they're doing. Totally disrespectful.

plasticpopcorn4... this is ummm captivating yet seems very unusable... but like it has been said.. maybe for future use. isnt the instance of the apple being divided by 0 posted by Mahesh Sooriarachchi not 0/0? it would live 1/0 right? and HOW CAN YOU wreck THAT WHICH IS NOT THERE? cant the respond just live no solution? haha. draw a picture, give it a name... voila YOUR A GENIUS. i guess this is kinda disgusting but i really dont observe a use. And too how can there live a point off of the number line? does that live substantive its not really a line but a graph?

TwasbrilligAre you actually kidding me? He made a original symbol, he didn't change mathematics. "Oooh, behold at me, this is a huge discovery: I can draw a original design!". This is actually sickening. Now every person is going to fade around "changing mathematics" by saying that a picture of their kisser means some previously unknown number. Give me a break.

DysanHa! Math has already stated that any division by zero is undefined, he just took infinity and null and just made a fancy original word instead of using undefined. I'll wait until this computer science teacher gets peer reviewed by the mathematics dept and publish a paper before he goes out and runs to the media, and recommend him that he should beget learnt that in first year calculus course, and should tarry out of the realm of mathematics.

Vaiti0/0 = Nullity Okay so what ??

JohnThis is not a 1200 year antique problem, nor is it newsworthy. every lone he did was allot a (meaningless) attribute to something that was equally meaningless, and do a few axioms for it. sure maybe it's useful in computer science, but it's nothing that a programmer with a cramped math background couldn't consequence himself. Teaching this to 10th graders will only agonize them, because they're going to contemplate that there's some actual numerical outcome to the arithmetic operation of dividing a number by zero, when it's really just a attribute that someone made up and tacked onto the extended reals. As my analysis professor said "definitions are neither upright nor false, they're either useful or not useful". If Dr. Anderson's axioms beget some kindly of exhaust then sure exhaust them, but they're certainly not newsworthy, and they're certainly not a "solution to a 1200 year antique problem that Newton and Pythagoras couldn't solve" as this article makes them out to be. Either this guy has a friend in BBC news, or they really necessity to consequence more homework on what they declare to live newsworthy. Is it so hard to google something and find out that the mathematical community thinks it's garbage?

Ajeet S. AroraHi, As they can understand that every lone mathematical function are the assumptions of one or more mathematician. as they said and did they are following that and if 1/0 could live infinity and -1/0 could live -infinity, so its an suited view he as proposed which is very simple that they should define 0/0 is something and that is nullity and which is quite ratiocinative even. So what no one can contemplate of in these 1200 years, they should fade for his theorems so that no calculator and computer should recommend us on dividing on zero that function is not defined :) atleast they know now there is a result ... Better luck. distinguished Work

Robert BeaubienThe respond to divide by zero is infinity, not nullity.

Matt GreenDIVIDION BY ZERO IS IMPOSSIBLE BECAUSE MY CALCULATOR SAYS SO AND IT IS THE TRUTH

Andy JoshHow is this original fangled "nullity" in any course different from the "NaN" (not a number) concept used in computer science for eons? It sounds the same.

BluE DicENullity has always existed, it's just been known as 'undefined'. This guy is no genius, he's a fraud.

AnonymouseThis is a joke, right?

D.S., GermanyI'm not quite sure if this person has create out something so "easy" and "basic" that no-one else seemed to care about or if he just "solved" a non-existing problem... Either course I'm really offended that he uses the kindly of dull title "nullity" - how would you translate that into other languages? For instance German: "Nulligkeit"? Yes, it _could_ solve some bad-ass problems somehow... But I contemplate it will live some 100-200 years that mathematicians will _really_ start to exhaust "nullity" ;)

a.c. coolwhat about nullity/0 ? i dont contemplate that the people with no mathematical background should remark unless youre asking a question. they just behold stupid.

Anonymous lofty schoolerwhats really so special able this? its like the square root of -1. its set outside of real numbers. can you set nullity into a graph? can you incorporate it into the unit circle. what beget you changed? as far as i'm concerned you've just renamed "no solution." and now your students contemplate your a genius. well, i'm going to rename you nullmind until i observe your "theory" actually used for something. are computers going to live less confused with a definition of nothing? wouldn't nullity itself occasions the computer to crash? i contemplate you should check out both sides of the coin before you pay your students with it.

DoctorBProving beyond any doubt what so ever that 0=0. Bravo!

PabloHungryHe stated that 1/0 equals infinity. In the third line from the bottom of his proof, he multiplies this infinity by 0/1. 0/1*infinity equals ZERO. Not zero over zero. Zero. Which is how many chicks Dr. Anderson is getting.

Acidhorsei did that once. a while back when Windows would boot up i started recieving an mistake message "cannot find file xxxxx" (divide by 0) Windows would then suspend at that mistake message. (ERR). so i solved the problem. i created a .txt file and named it whatever file Windows was looking for and dropped it into the System folder. (nullity) WOOT !!!1

ColinYesss, I contemplate I grasp this concept. Wait! I just saw myself going out as I was coming in. do it stop. do it stop.

Chris DrostHe apparently demonstrates no information of any advanced concepts related to his present situation. There's no mention of the fact that if f(x) and g(x) both fade to 0 at some value x*, the restrict of f(x)/g(x) near x* might live any complicated number, or could even live infinite. They solved 0^0 a long time ago. It follows the profile x^y, and has two different limits depending on whether you route x to zero first (because 0^y = 0 for every lone y, so the restrict is 0) or if you route y to zero first (because x^0 = 1 for every lone x, so the restrict is 1). We've further established that, in the most generic case, the "best" restrict for this scenario is 1, though technically the view isn't completely coherent because the restrict doesn't really exist in the 2d space. If x^y, for nonnegative real x and nonnegative real y, is actually giving us numbers off the real line, then they necessity to live worried, friends. Finally, you cannot define addition, multiplication, subtraction, and division in the criterion course while still keeping nullity "off the real line." If basic arithmetic operations are allowed on nullity, it can live proven that nullity is any real number that you want it to be.

OmarI just invented a problem to an "error" of science that neglects to respond the question of how their universe began. The respond is an knowing designer. This designer lies outside their skill to perceive or commemorate it directly, and its essence cannot live isolated in a lab. By giving this concept the title "intelligent design," I've solved one of the Earth's oldest questions! Mr. Anderson's "theory" of "Nullity" is just about as useful. Those destitute children.

ericthis is the most pathetic attempt at proving something i beget ever seen. the entire prrof relies on dividing by zero which is impossible and cannot live proven otherwise. this is a shame to even give this man any notoriety and BBC should net rid of this before anyone else wastes there time and reads about it.

Adam1/0 does not "equal" infinity. -1/0 does not "equal" negative infinity. desist treating infinity like it's suddenly become a quantifiable number that can live used in arithmetic. Sure, you can pick the restrict with either, using c/x as x-->0, but that still doesn't define what the result really IS at that point. every lone he's done is exhaust rudimentary algebra to net 0^0 into another form, 0/0, to which he just recently assigned a bogus symbol. And now he's teaching it to students, as if it were real mathematics?

James MarinoI came up with a similar theory a few years ago during math class when i noticed that infinity and undefined on a two dimentional graph looked the very (they are the very according to me . . . they are just the opposite ends of infinity) buckymarino@gmail.com

JeffI beget a Master's degree in Mathematics from a well-respected university in Missouri, USA, and I observe what Dr. Anderson is doing here. The problem people are experiencing with this stems from them assuming Dr. Anderson is using the notion of "infinity" and "negative infinity" by the ideas utilized in calculus, where they can multiple these by any positive real number and it stays positive or negative infinity. Similarly, if they multiply them by a negative real number, they net the opposite. However, by defining 1/0 as infinity and -1/0 as negative inifinity, Dr. Anderson is distinguishing 1/0 as infinity, 2/0 as 2*infinity, and so on, where 2*infinity is NOT EQUAL TO infinity. Using Dr. Anderson's logic, inifinity plus negative infinity equals nullity. Thus, nullity does exist as an extended real number. It's much easier to observe if you view infinity and negative infinity as being real numbers themselves, not the abstract concepts they learned in their basic calculus courses. You every lone bash Dr. Anderson and stutter he is trying to recieve credit for a pointless idea. He has just shown that there exists another extended real number!

Holy GoogamookPhwoar this guy roxors my world! this has Nullity uses, and eternal amount of strangness.

The DripSorry I am so late guys but I figured this out. Zero is not a number, it is a belt holder for where a number would be. I can't dole a number no times. This statd, I can not dole nothing no times. Therefore any number dividing by nothing is equal to The Drip. This is a revolutionary number that stands for "anything you want" because the drip delivers.

JMI don't live substantive to live rude, because I like to try and discover things as well. I dont observe a solution here, every lone I observe is a made up number that replaces what was already there! Basically, zero was defined multiple times and then just made to equal some made up number...? On the topic of mechanical problems, they only exist because they recommend them to. There is no magic behind a calculator erroring out...we gave it that error! So dividing a number by zero has just been given a name..nothing has been solved here.

Brett BI admire every lone the comments of people complaining that nullity is bull because it's not on the numberline. Progress comes from thinking outside the box people

Andrew GreenThis is a shame to math, math isn't hypothetical to live facile and quite frankly find it insulting to find you mocking math greats by belittling them as inferior to school children's minds.

ChuckThis is useful, but it's impossible to recommend from the article. If you actually know math, read his articles on bookofparagon.com to understand the closure and definition of the operations on an extended number line.

EltharionI'm just going to train my students that 0/0 = pineapples and then 0^0 = 0/0 = pineapples. Don't you see? This guy just gave 0/0 another NAME, not a solution.

ZaratustraMATHEMATICS DON'T toil THAT WAY

Sir. Edwardnullity.. ti's crazy.

Joe SippleObviously this guy knows nothing about computer science or mathematics. Nice try, and thank you for wasting my time BBC.

Per Alltrelén(razorstar@hotmail.com)Zero or nonexistence can't exist. That nonexistence in the very time should exist is a greatest ratiocinative paradox of them all. Therefore should't they construct something which not exist in the reality.

yy2bggggsOkay, let's slay nullity. I know a trick--we'll multiply by 0. 0^0 = 0*(0^-1) = (0/0)*(0^0) = (0/(0*0))*(0^1) = (0/0)*(0^1) =nullity*0 = nullity (see above) Huh? Okay, nullity cannot live killed. That's fine. Maybe I should just try to avoid it. Let's just try everyday math. 2+2=4 2+2+0=4 2+2+0^1=4 2+2+0*(0^0)=4 2+2+nullity=4 ARGH!!! Well, thanks a lot, mister anderson, for disproving math. NOW what are computers hypothetical to do?

ChanduI don contemplate this just works out! Now how consequence u define nullity and its subsequent arithmatic? Does proposing a original hypothetical "Nullity" solve this? Hmm I don't know! Kudos to every ones comments below!

KevinIf Dr Anderson was a solicitor (or an attorney in the USA), he would beget asked what number they wanted 0/0 to be.

president of chinayour dispute is invalid

SaneCongratulations! You just invented QNAN, +INF, and -INF! What the hell is this nullity word?

MPrattThis idiot fails to recognize that anything divided by zero is infinity. They know this allready.

Richard ShetronCDC computers beget been working with 1/0 since the 60's. I don't remember the replete details, but in addition to everyday results from math they too beget flags on every word that bespeak if the result is x/0 or -x/0 so division by 0 does not bear an error.

ATWhile this is an captivating theory, I would like to observe a paper or some profile of actual hypothetical toil other than writing on a chalkboard. I am highly suspicious that he is indoctrinating his students with his theory rather than giving talks to the more mathematically developed.

B. BabicWait, so in other words nullity is undefined? He just renamed a well-known principle; is he clinically insane?

Jenna at EJSHS!!!This guy is replete of crap. He hasn't solved anything. What I thought was amusing was that one of his first sentences, he was trying to define nullity and he said that it was a number that was off of the number line. WTF?!? Am I the only one that noticed that in one of his first sentences, he proves himself wrong. The number line is exactly what it means, every lone of the numbers. . . ever. . .INCLUDING INFINITY! Also, making up a 'problem' and making up an respond ISN'T SOLVING ANYTHING! Something else thats amusing is that I'm only a freshmen in lofty school and in algebra I honors.

John DillingerYes, but try getting a computer to understand "Nullity" :) It doesn't really beget that much impact on real mathmatics at all.

KamalHow to define in basis two? Because computer system works in binary level. If you can please clarify how to define n basis two or any other bases.

Anonymous CowardI can't believe BBC would publish this crap. People stutter that complicated numbers were criticized, and behold at them now! The only dissimilarity is, complicated numbers actually meet in with the postulates of arithmetic. Quite simply, we're looking at a number n such that n=0/0, sense that any number c*n = n. c could live any number. Now, let's divide both sides by n. We'll live left with c=n/n. What's the only number where dividing by itself is any number? 0. Therefore, n=0. So, we're basically saying that nullity is zero, but, on the other hand, it could live any other number, too. contemplate about the logic behind division. What number times zero = zero? If you said any number, you're right. So, we're saying that nullity is both zero and every number at the very time. Anyway, it's facile to prove lots of things using Dr. Anderson's theory, but it's really just a lot of crap. Oh, by the way, anyone who wants to exhaust the instance of a pie being shared between zero friends, stop. If you beget 1/0, nothing times 0 is 1, so you're wrong.

TreyThe problem with dividing by zero is that zero is not a number, its a concept- it has no value, no real actuality outside the view that if there's nothing of something than theres 0 amount of it. Likewise, infinity and negative infinity are concepts, not values. Thus what he's essentially doing is giving a concept notation (example:-1^(1/2)). He's not really doing anything that much different. The only real practical application would live to do it a value that calculators can understand (which, by the way, just gives programmers a giant headache trying to clarify to a machine that what doesn't exist now does and has been given some value). I just don't observe how useful it is as most computers are told to reserve every lone zeros on top.

John VanDammeWow, they came up with something that was totally unneeded, since you already can divide by zero in higher math.

SelGreat..... Another course to do math complex.... I knew there was a intuition I hated it lol.

Wile E. CoyoteThis is so simple! He states the sense of nulity birthright up front in the discussion. Nulity lies off the number line, hence it is non-numeric and unmeasurable. if x = 0/0 x therefore is Nulity hence x = a fish Nulity is surealistic mathematics. Duh!

Agent Smith"You beget a problem with authority, Mr. Anderson. You believe you are special, that someway the rules consequence not apply to you. Obviously, you are mistaken." -- from The Matrix

DisappointedSo, I've been ranting about every lone the holes in this proof for the past two hours to a few friends of mine, and it finally struck me why this was so frustrating- he's using circular logic to prove his "nullity"! He starts out telling us that "0/0 = nullity" and then ends with "0/0" saying "Oh, then this must live nullity, I was right!" (As a side note, I phenomenon if he shouted "Eureka!" when he figured this out?) According to the logic presented in this proof, if I cannot solve a problem, I can rename it. Problem solved. It's like Mitch Hedberg joked: "If you are lost in the woods, then build a house. 'I used to live lost, but now I live here. I beget severely improved my predicament!'" This logic makes no sense. So because nullity can essentially live substantive anything, am I now allowed to exhaust this to respond every lone my tests? "What'd you net for number eight?" "Nullity." "Oh, man. Me, too. They rock." It doesn't do sense! There never WAS a problem with 0/0... 0/0 = undefined. I contemplate that this is basic algebra. I sincerely hope I am not the only one that is severely disappointed in Dr. Anderson for this fallacy.

BazMe thinks too much fish oil in the diet is to foible for this. Anything divided by zero is an indefinite number, that is the result is unknowable.

Brian Brian Bo Brian Bananna Fanna Fo finnan Me MiDamn you earthlings!!! You finally solved the enigma that has allowed for humanity's enslavement and kept mankind in perpetual ignorance. The light of verity has finally been revealed and means the undoing of your extraterrestrial masters' hold on your souls. For ever, the name, Dr. James Anderson will resound light-years throughout the universe, bringing enlightenment to every lone that exists and doom to every lone that stands in it's way-- kindly of like when Rick Moranis went "plaid" in Spaceballs.

Annoyed.ram? I want to laugh at this lunatic, but not badly enough to exhaust real Player. Ugh. I contemplate I'm gonna live sick...

PeterHI am a math guy and a computer guy. There's not enough information here to do a judgment. I could observe where it might live useful, but there's not enough there to live convinced. For instance, 1/0 = infinity in the sense of restrict N as N approaches infinity? That's not necessarily true, depends on how you consequence 1/0. If you pick 0 to live the restrict of -1/n where n approaches infinity, his infinity is the opposite of mine. Also, is this essentially a computer science issue or a math issue? From a math point of view its really missing a lot that I don't contemplate can live fixed, but from a CS point of view, with some definitions of 1/0 and -1/0 this might live useful. In otherwords, how would he submit to implement this in hardware?

fedematicoTo divide by zero it's too really .... egoistic!

Ben DavidSo essentially what I net out of this is that "nullity" is another course of writing d.n.e. Even if you were able to exhaust l'Hopital's rule and not find an answer, the result would live undefined or "does not exist"

TheEngineerThis should live in Wiki as definition of FUBAR. I'm not kidding...

Douglas SmithI'd like to observe how these school kids prize this nullity crap when they net to calculus, and beget to start actually bothering to solve for the restrict of 0/0, and not writing down "nullity". I mean, I guess I'll define infinity/infinity as Super Infinity or something while we're at it.

Øyvind KarlsenI am sorry Dr Anderson but "nullity" is the very as zero. behold at this; 0*0=0. Dividing by 0 on both sides and you net 0=0/0; zero = "nullity". Or in words; 2 dolars to live divided equally between two persons, how much will each get? 2/2 = 1. 1 dolar to live divided between one person, how much will each get? 1/1 = 1. 0 dolar to live divided between zero persons, how much will each get? 0/0 = 0 (no one will net anything).

Seth DixYou infuriate me, Dr. James Anderson. You are just as snide as your kids who will respond your questions to prove something in class with, "X is upright just because it is." I guess your solution could live considered a "rhetorical answer," if such a thing exists. If not, let's define capital Phi = "rhetorical answer." Thanks for ruining the next generation. These kids will live amenable for the world when I gain the very point of senility that you clearly beget create early on in life.

AlexFrom scrolling down a few lines, I can recommend that this is redundant. But really, the BBC is accepting this sophistry as an innovation? "Nullity" is only a means of symbolising the results of shoddy programming - any discerning mathematician would just apply l'Hopital's rule if he wanted to solve anything.

Dr DodgyPerhaps "Nullity" is the hidden sense of life, cos i can't observe it having any other use.

Joe FrischThis has already been done, and in the birthright ways. Don't congratulate the guy for inventing nonsense, he's just going to befuddle his kids.

Guy TanzerI'm not a mathematician. I fix and program and train computers, and got into computer to net AWAY from higher math. This is probably flying lofty away in some ethereal, rarified height of mathematics us mere mortals never observe and cannot appreciate. But it seems to me that yes, you can theoretically remove 0 from any given number an eternal number of times.... but if you're removing 0, are you actually doing anything at all? I can, in theory, write an eternal number of $0.00 checks from my account and route them to everyone on Earth.... but every lone that would chance is my bank would net very vexed with me. Maybe there will someday live something to consequence with this wondrous original discovery, just as i is used in electronics somewhere. But until then I contemplate this is just a bag of wind. Matthew McDonaldI once saw an equasion that, while individually every lone of the internal equasions were correct, the resulting respond stated that 1 = 0. The exhaust of an informal falicy while "logically" working out the problem, was the occasions of the flawed final statement. I believe this falls into that very trap. As stated many times by other people here, anyone can behold at an unanswerable problem, add a magical constant, and do it work. It still does not respond the problem, it just makes the solver behold suited and dissipate the time of other, legitamate mathematicians who now must try to prove, or disprove the solution, which was never valid to start with. LulzYou made the universe explode PiersOf every lone the 1200 years gone by, contemplate of the amount of people during that time that would beget had the very concept of making a original number to solve it but havn't expressed so becuase it's such a cheap method. This Guy is an IdiotI beget invented an imaginary creature. It is called the distinguished Lintughler of Blogenia. This creature does not exist, so instead of calling it The distinguished Lintughler of Blogenia, I'll just muster it &#8362;. Now they can study the &#8362; as if it were a real creature. "Nullity" is really just a shortened profile of ERROR: DIVISION BY 0, and is no more helpful. A concerned AmericanThis Mr. Anderson should desist teaching kids garbage and fade trisect an angle or something. EEAdding a original number like this is a bailiwick extension of C, which is impossible. ShawnWhat a quack. There's a intuition this guy doesn't present this at a mathematics conference or publish the finding in a journal. Because anyone with limited mathematical information can observe through this. And it's so glaringly obvious that no one bothers explaining why it's wrong. BBC bought this from an attention-craving fool hook, line, and sinker. Maybe he's not so much a fool for having planned such a publicity stunt. Perhaps one can stutter that his mathematical career is ruined, but I doubt he had one to start with. Mattwhat a joke... the bbc should live ashamed they published this... JohnHis solution appears tautological. What is 0/0? Nullity. What is Nullity? 0/0. It has the feel of imaginary numbers, after every lone i is not really a 'solution' to the problem of the square root of -1, just a title for it. But since anything times nullity is nullity, there's no 'nullity' number line in the sense that there's an 'imaginary' number line. It looks like simply a title for the connundrum, and not an actual solution. Addmitedly, I suppose it would live an odds to computer science simply to recommend the computer the respond was some made up concept rather than throwing an exception. I= hella smarter than Dr James Andersonokay how is this on bbc news... he just rule a title for 0/0. but the verity is this is every lone wrong 0/0 is actually dumbassity Nelson SelingerVery interesting! LukeThis guy basically made a original title for "undefined." James DobermanIts disappointing that a trait newspaper such as bbc would not realise what a destitute trait article this is. They should really rush this past an academic (or even impartial lofty school student) before publishing. MattI beget one major issue with what most of you are saying. 1/0 does NOT equal infinity, it is undefined. if you want to pick the restrict of 1/x as x approaches zero, then it APPROACHES infinity. You can't beget anything that is explicitly equal to infinity. In mathematics, even infinity does not exactly equal itself. Infinity is a term used to define a generic, indescribably big number. It isn't meant to live used as an actual number. NoelSo basically it took a Dr. to develop a problem school children can do, because they'll know that Nullity = 0/0. which means, 0=1+(-1). So 0/0 = (1+(-1))/0 = (1/0)+(-1/0) = Infinity + Negative Infinity. Which every lone together now = 0. So why not just desist at 0 and deliver those destitute school children some pencil lead and a headache. MarkThis is a horrible excuse for mathematics. So this guy took a concept that was already known (i.e. you can't divide by zero) and deliver a title on it. And called it a theory... Also, what the heck is up with the "If your pacemaker divides by zero"? Does he contemplate every lone programmers are retarded? John SpartanSo if -1/0 is negative infinity, then 0*(-infinity) = -1? If so then what does -2/0 equal? -2*infinity? So now you are able to multiply infinity by numbers? Well I guess you can, and then stutter that 2*infinity>1*infinity. But is it so feasible to consequence ANYTHING to infinity since it's already infinite, a number with no exact value. JHIt looks every lone right, I still beget effort with it though, maybe im too used to the real number line. Is this just an "official" title and attribute for an indeterminate? NoelSo basically it took a Dr. to develop a problem school children can do, because they'll know that Nullity = 0/0. which means, 0=1+(-1). So 0/0 = (1+(-1))/0 = (1/0)+(-1/0) = Infinity + Negative Infinity. Which every lone together now = 0. So why not just desist at 0 and deliver those destitute school children some pencil lead and a headache. RyanThis is just asinine. every lone this prof. has done is supplant the word "Undefined" with "Nullity". They already had a course to express 0/0, they just didn't muster it a solution, - because it's not - it's a representative term, and so is Nullity. I created a solution for 1/infinity: I called it "fhqwhgads", can I net a medal now? nyetsheblatThrows division by 0 Catches Nullity. A by-product of infinity, the computer continues to process forever, no longer remembering to reserve the plane from crashing into the ocean. Its too diligent doing eternal mistake handling. thanks a a lot. It feels like binary in basis 3. Kyle S.I contemplate he is just trying to live cool— and being really dull in the process. FrankWow. Terrible. I am ashamed for the bailiwick of mathematics. jasonso suddenly zero divided by zero is a nullty? would that uphold anything, i live substantive to say- would that consequence anything besides pick a title and attribute for "undefinded" zero divided by zero isnt going to start being one, it is just a title for the non named mistake that is "undefined", so would it actualy uphold out the math world at all? W LWow... this really is a complete dissipate of site space, though I guess BBC you succeeded in getting people to visit your site and require "What were you thinking?" Steve BakerCOmputers don't beget to crash when they divide by zero - almost every lone of them consequence this as a courtesy to the programmer since no well-thought out 'real' thing every requires you to divide by zero - so it's almost always a bug - and you WANT the computer to crash so you can find the bug and fix it. If your pacemaker is dividing by a number that can every live zero then the program is already faulty for some reason. When you consequence want to divide by zero, you can recommend the computer's operating system not to crash the program. The IEEE criterion for what the computer returns when you consequence this is called "Not-A-Number" or "NaN" for short. This is effectively the very as this guy's "Nullity". Mathematically, this guy is talking nonsense...and teaching it to kids before it's gotten widespread acceptance in the mathematical community is temerarious stupidity. KatherineThis is completely ridiculous. This isn't math at all. jamesum, every lone he did was approach up with a "new" number. Could beget called it "X" and it'd live the very thing. And yes, nullity can live any number, so if you beget 3*0=0 and you divide 0 from both sides you net 3=nullity. Now i can never live wrong on my math homework! Carl MelZero's zero's and more zero's! If I banged my head birthright now, I'd observe zero's instead of stars!!! MartyThis is absurd. As x approaches zero, then 1/x approaches infinity. Infinity is a concept, not a number. Undefined is too a concept, not a number. every lone this guy did was do up a title and a attribute instead of saying "undefined". Even if somehow, somewhere, what he is preaching is useful, what he has done is not at every lone original. This is just another instance of idiots with PhD's going around confusing people and making the real scientists of the world behold bad. brian griffeyNo, that's not mathematics. I'm graduating in may with a degree in mathematics and that proof doesn't live substantive anything. He is just defining his "nullity" to live 1/0 which isn't a number which means he hasn't solved anything. Anonymouswhats the point of dividing by zero other then to fool and trap your enemies into a time paradox? buahahahathis is so my away message for the next 1/0 days. And the Quotes, OH my goodness the quotes! Those kids, I feel pity, oh so much commiseration for them. RolandYou know, I had this view ten years ago in lofty school. I told everyone involved with the math department and they every lone told me it was "stupid" and "useless" and "not mathematically relevant." Why can't my ideas live accepted and considered valuable just because I beget a cramped piece of paper that says I spent 8 years in higher education? EngineerYOU SUCK. There's no exhaust for a creation of another view to delineate a divison by zero error. Any competent engineer or programmer would beget coded a prevention system in belt to prevent dividing by zero in an airplane or pacemaker. Your examples are nullified and your purpose is useless. SekkyThis man is a computer scientist, not a mathematician. I can't believe these kids are buying into to this garbage. I too can't believe that this man can believe that nobody else has ever thought up of giving a original damn title to an already existing concept, especially considering how NaN already exists and he is, supposedly, a Doctor of computer science. NaN works well, this is simply a dull relabelling. Of course you've 'solved' it, you defined it that course in the first place! I dare him to route his into MIT, Cambridge or Clay, they'll shoot him down in seconds. BBC you should live ashamed to beget featured this, unhurried day for word was it? BenAmazing, Dr. Anderson has solved a problem that "hasn't been solved for twelve hundred (?) years," that "Computers simply cannot divide by zero," unless, you know, you exhaust a *computer*. The BBC, improbable people who don't understand IEEE floating point arithmetic for 84 years and counting! MSJI'm ashamed that BBC would publish such bull. search a better mathematician's recommendation before lauding this crap. DWHah! I did this months ago, bored in Calculus class. Actually, I contemplate I defined 1/0 to something. Whatever, point is that it's meaningless. Haha, at the time I defined the set of numbers including my original number for 1/0 as the "Ridiculous Numbers"... Hanno EssenI consequence not contemplate that Dr Anderson's theory is entirely new. Yaroslav D. Sergeyev of the University of Calabria, Italy, has published similar stuff at conferences and has a patent application. AlphaThe only thing I observe in that proof is that 0=1-1. And ... 0^0 should live 1 from what I remember ... then he proves that 0^0 = 0/0 = NULLITY? would that imply that NULLITY = 1? not very convincing :) YankeeThis isn't even a story. Mathematicians beget understood this concept for years. He's giving another title to something that already exists, and teaching it to kids. Daniel PalmerYour peacemaker might crash if it does a divide by zero and one of the following properties are present; - The MCU running the code doesn't exploit divide by zero or the logic to exploit it doesn't toil (this has happened in at least one MCU, don't know if it was ever used in a pacemaker). remember a divide by zero would result in a eternal loop and alsorts of nasty things could chance :/ - The software running on the MCU is broken and isn't catching the divide by zero when the MCU flags it. I'd hope pacemaker designers test their code... People aren't seeing the Big pictureThis does actually beget practical applications in terms of computer science. Just because it isn't useful in everyday life for most of us doesn't live substantive that it has no value whatsoever; as mentioned earlier, they can disparage "i" as useless, when it's very useful in specific settings. Congratulations to Dr. Anderson for reaching these conclusions; while I'm sure it must live disheartening to read every lone these comments dismissing his research, those of us who understand more about the problem actually observe how useful this is. reserve up the suited work! Ken Steinthis is retarded, computers beget had an mistake flag in the FPU for this for I dunno... maybe thirty years now? it's called NaN/Not A Number and does the job just fine. This "researcher" just came up with a dumbass title for something that already existed, he didn't invent anything. jdWhen I did this in lofty school math class, it was rejected. I was told that it was not a valid method, was against the rules, et cetera. Why is it he gets to net away with this and not me? AnonymousWHAT HAS SCIENCE DONE? THAT FOOL, EVERYONE KNOWS THAT BY DIVIDING BY ZERO CREATES A TIME PARADOX, CAUSING THE UNIVERSE TO IMPLODE! THOSE unlearned FOOLS! JohnI agree, division by zero is not a problem for computers, it's a feature. Programmers can override the mistake interrupt, belt zero as an respond or exploit it by other means. Prof. Finkelsteinyou can't define inf= 1/0. becasuse then inf*0=1 and zero multiplied with anything "kills" anything, i.e. inf*0=0. so: 1=0 ? answer: no! Mark WagnerNow that I've had a chance to behold at this from a grave mathematical perspective, it makes no sense. Yes, he's managed to do dividing by zero give a sensible result. But in doing so, he's thrown away most of the properties that do traditional arithmetic so useful and facile to use. In abstract algebra terms, he's invented a set with two operations -- about the most primitive sort of mathematical system possible. BI beget deviced to rename 316 to "Brian" - is that ok with everyone? emo kidGreat, now not only consequence they beget eternal depths of human sufferings, but now they had nullity depths of human suffering. Excuse me while I fade prick myself. Wathel Bloture-HernessThis is just more liberal propaganda that's trying to remove us farther away from God. University of Toronto's computer science departmenI feel snide for those pupils and for the fool that thought James Anderson should beget "Dr." in front of his name. consequence they not train calculus in England? Any non-zero number divided by 0 is infinity. Let y = 1/x. As x approaches 0, y approaches infinity. Furthermore, the expression "0/0" is an "indeterminate form". That does not simply live substantive that it is undefined; rather, it means that if f(x) and g(x) both approach 0 as x approaches some number, then f(x)/g(x) could approach any finite number or infinity or negative infinity. It depends on which functions f and g are. observe L'Hopital's rule. The intuition simple calculators note an mistake is because infinity is too big to store in remembrance and too because they haven't programmed L'Hopital's rule into the calculator. A real computer scientist would know that this "problem" was already easy. Mr. James Anderson is just trying to do it complicated. PirosWow... I guess even the BBC has an off day. TylerA number 0/0 is called an indeterminant form. So is (inf)*0, 1^inf, etc. Simply multiplying both sides by infinity (with the lofty assumption that infinity is a number), only results in another indeterminant form. Expanding products of 0, 1, and infinity again will only result in more indeterminants. every lone of the people that posted "proofs" did not necessarily consequence anything wrong, but the result is misinterpreted. As for every lone of the "proofs" that nullity is a fallacious view pick into account similar lofty assumptions. That is to say, Dr. Anderson did not stutter where "nullity" belongs. He only said it was off (what I assume to be) the real line. He, for some reason, didn't define any rules of combination for this number with other numbers, what its properties are, etc. From the video, it is not clear what you should live allowed to assume. Ben KershnerThis is one of the dumbest things I've ever read. Where did this guy net his CS degree, ITT Tech? Wait, that would live a disservice to that reputable institution. NoraThis is, sadly, the stupidest thing by far that I've ever seen 'reported' by the Beeb. Dr. Alkhwaizmi typing from my wheelchair.So this nullity thing, does it vibrate? Will it net rid of George Bush and TomKat, solve global warming, net me a Wii and establish World Peace? If so, I am every lone for it. No matter how impossible it sounds its just a matter of enough of us believing in it, by virtue of which the impossible comes into the realm of possible. I Believe. ComputerScientisthaahaahaahaa... I am cheerful i did not fade to Reading. Does the author beget tenure ? BenDr Anderson has done cramped but allot a title to an already well understood concept. They muster it 'undefined'. changing its title doesn't change the problem. This guy calls himself a computer scientist? dantes_tormentThe concept doesn't seem much different than that of i, and it's considered useful in the math world. Unfortunately, he's made a Big deal out of declaring that 0/0=0/0=nullity. Any number x^0=1=x/x; so obviously 0^0=0/0=1? This has an unreasonable amount of proof to note what would pick a few moments of common sense. Why allot "nullity" to what can live proven to live 1? And division by zero we've said is infinity; and it's obvious x*0=0, so 0/0=x. This means 0/0 is any concievable number. It's suited in theory, but what he did is unnessicary. ShaunWOW. I wish i could do up numbers. PavanHow can they allow someone to train impressionable students a controversial topic without a peer review. I remember in 3rd grade, my (substitute) math teacher using '' (greater less than) in the opposite sense and until quite a few years after, I used to live confused while using them. What I am saying is that it is hard to 'unlearn' something so do sure you don't experiment while teaching basic concepts. Donald CallowayI'm a mathematician, and like Star Trek's Mr. Spock, I say, "fascinating!" I phenomenon what nullity to the nullity power would be? It's a number that is its own reciprocal, no? If so, then nullity squared is equal to 1, no? In fact, nullity to any power is equal to 1. But 1 is a number that is its own reciprocal as well, just not equal to one. First Time ReaderOk, I finally tracked down the paper where he outlines his arguments. Looks like the real numbers + nullity + some other infinities = the transreal numbers, and given the axioms of transreal arithmetic, you *can* divide by zero. every lone of the criterion proofs that you can't (some are mentioned in this remark thread) are addressed in the paper, and he shows how they rely on assumptions in the axioms that are avoided in the axioms for transreal arithmetic and transreal analysis. Because transreal arithmetic can consequence everything criterion real number arithmetic can do, yet can too exploit corner cases that often approach up in scientific computing, he's arguing that they amble the floating-point numeric format for computers to conform with the transreal number axioms. Richardwhat a joke Terje van der MeerenSo when you divide with the original number "nullity" which is outside the conventional number line, what consequence you get? Another number "infinity" which is too outside the number line? Dr Neil GreenIm a mathamatics lecturer at Oxford University, i was emailed this page earlier today, and simply nothing has been solved. every lone has been proved is any number multiplied by zero = zero. As if 0/0= "nullity", "nullity" * 0 = 0, so numity is just representing any real or complicated number. Altho nothing original has been proven i can observe how it might live useful to 'lable' this singularity 0/0. But simply 0/0 is equal to any and every number every lone at the very time. In this case "nullity" is everything. RajivThis guy is a *** idiot. He just gave a original title to something that was already known. He has not solved anything in terms of math or computer science. It's dismal that it takes so cramped competence to beget a degree in computer science. Carboon MontleyAnyone can do up a number to solve a problem. That takes no skill at all. like 2^x=-4; thats impossible. But if x={}, some number i tow out of my rectal cavity, it works. MattEven if Dr Anderson's theory is not nonsense (I am not qualified to judge), its "explanation" on the BBC website certainly is. AndrewHe's simply renamed the term "undefined" and called it "nullity". That's hardly news. Maybe I can solve the problem of cancer by renaming it "consumption". LMWhen he says he's 'solving a 1200 year antique problem' I'm pretty sure he means it lightly. He's just defined nullity to live equal to 0/0 and showed a few different ways to delineate 0/0. To a mathematician this is no more useful than saying x = 0/0. In fact it is no different. However, it seems like his students are interested in what he's teaching. I contemplate I'd prefer to beget a teacher recommend my children to study real analysis when 0/0 comes up. Of course this is coming from someone who would live pleased to uphold an inqusitive student toil through Baby Rudin. Although, that may live a bit past the age and even of these students. ADanWho the heck was doing math 800 AD? Blake L.Uh.. What happens when you Divide Nullity by Nullity or any number (zero included) by Nullity? You beget the very problem. Gary PatellaAlthough I hold no degree in mathematics, I am fairly well-versed in the subject. After reviewing Dr. Anderson's demonstration, I felt that he has accomplished absolutely nothing. His so-called "theory" merely takes a quantity considered undefined and renames this quantity nullity. Dr. Anderson merely fiddles around with basic functions in his demonstration. He starts out with 0/0 and through unnecessary steps that can live applied to any variable, arrives back at the very number. The pretension is that renaming this quantity "nullity" solves every lone of the problems that this value has previously encountered. But it does nothing of the sort! It is analagous to someone trying to do the square root of two rational by renaming it a/z. Taking this number, multiplying by 3, adding 5, then adding six, then subtracting eleven, and finally dividing by 3 will bring one back to the very quantity. But this does not prove, nor does it solve anything. In short, Dr. Anderson's "theory" should live rejected by the mathematical community. TJSo basically this "Doctor" Anderson has substituted the term "nullity" for what would normally just live an undefined outcome. This is not new, and he has approach no closer to solving the "nan (not a number)" problem than Newton or Pythagoras or anyone else. This article is ridiculously misinformative and needs to live taken down. stupid theorywhat if you were to consider someithing divided by nullity 6/nullity=????? this total theory is stupid okayI beget a B.S. in Mathematics, NOT a Phd but... This guy is a Doctor? Pacemakers and aeroplanes dividing by zero? sure thing dude. sups0/0 and x/0 are not limitations of math nor computer science. They are undefined. And that is not to stutter that they hope one day they will live defined... NO! They are undefined for VERY suited reasons. Computers can already exploit infinity, undefined, NaN , and i on an application by application basis. When you beget x/0, there is no mathematical respond which will meet every situation. Sometimes you'd want to terminate, or re-do something, or try the next item, or require for user intervention, or set the result to 0, or to 5 or to -999.999. It depends on the application. There is nothing elegant about giving up and using "nullity" which doesn't solve anything! In calculus 0/0 could 'effectively' live 5 or -77 or pi. It doesn't really EQUAL any of those but you know what I live substantive if you know calculus. Stopping at nullity is stupid. It presumes you are using math for math's sake. Asking 0/0 = ? is like asking "Where did you net your hat?" when you DON'T beget A HAT. It's not sound to do AN respond FOR THE QUESTION, when they should recognize there is NO ANSWER. And there is NO NUMBER. Undefined. David CookAgain proof that reporters are dumb (and this CS teacher is even dumber). every lone he did is give NaN (Not a Number) a original name. FPU's beget had the concept of NaN for years. Giving NaN a different title in no course makes it a number - it still can't live used in math because it is NOT A NUMBER! Geeze... this is basic computer science - pick this guys degree away from him immediatly. what the heckSo, since nullity = undefined, 0/0=nullity=undefined, and since 0^0=nullity, 0^0=undefined. Where has this brought us? DNA'NaN' and 'undefined' beget existed on computers for years... How is this new? Void of SpaceI'm sorry but this is a solution that has been suggested by school kids since the dawn of time and been hammered out of them by the education system. Looks like the system missed one ;) As a fellow comp. scientist keeping an open mind, if he can net some mathemeticians to uphold him validate his theory then I'll give him credit...but only WHEN it's due. So nullity is the measure of how nothing, nothing is...sounds more like a rate of nothingness...perhaps irrate nothingness :P Dennis The TigerThe real trick is to divide the square root of any negative number by zero, and then survive the resulting black hole. SteveThis sage is an excellent Troll for artificial site content and comments. The proverbial storm in a teacup. Job well done. DNA'NaN' and 'undefined' beget existed on computers for years... How is this new? Mathew Guice"Nullity" is an captivating tern to give to a concept that already has 3 terms (indeterminant form, undefined and NaN - Not a Number). Being able to give a term and attribute to a concept that has been around for hundreds of years is not genius. If Dr. James Anderson could note transforations through "Nullity" that would live genius, but it appears to live just as un-useable as the other terms in calculations. If an article like this is to live run, please consequence your homework as to what the real isse is which is being able to transorm calculations through a devide by zero problem (which still cannot live done). John SummersonExcellent toil by Dr Anderson. Now every lone they necessity is a original title for the exact number that spans megative infinity to positive infinity. I shall muster it 'Allity'. Bow before it's Inexpressable Truth. I too submit that the smallest positive number above 0 live called 'Smallity'. Marko SeppänenIt seems like he has only renamed 'NaN' to 'nullity'. He has discovered a flat, round disc that already exists as the wheel (Not a Number) and given it a original name. Why invent the wheel over and over again? Erik NaggumThere used to live a rule in academia that you publish OR perish. With the introduction of this brilliant piece of software engineering into mathematics, Dr. James Anderson may redefine that rule to publish AND perish. Andy L.Somebody may beget made this point already, but I sorta glossed over after spending 15 minutes reading every lone the comments, LOL... The flaw I'm finding in Dr. Anderson's theory is that dividing by zero isn't bidirectional. That is to say, 6/3=2. I can reverse that with by multiplying 2*3 to net back to the original 6. How would you consequence this with an equation divided by zero? Unless I'm missing something, anything divided by zero would finish up as nullity, so nullity times 0=infinity. First Time ReaderWow, what a sensationalist article! I'm really disappointed with the BBC for spreading misconceptions about the nature of mathematics, and promoting this flawed "theory" as a mathematical revolution, when it's unpretentious to advanced lofty school students, and to any university-level mathematics or computer science student that: 1) Division by zero is *defined* to live meaningless because that's the only course to maintain useful properties of the arithmetic system, 2) that computers don't beget a "problem" with division-by-zero, but are *designed* to flag it as an mistake for the exact intuition it was defined meaningless in mathematics, and 3) making up a attribute for "0/0" is useless without creating a system of mathematical rules that is consistent, doesn't lead to contradictory statements, and is useful in application to mathematical theory or practical computations -- unfortunately, it has been *proven* time and time again that you cannot define division by zero without contradicting some other, more useful property. Anybody can do up any original system of mathematics by tweaking existing rules or creating a completely original set of rules. To live useful, it has to either prove something novel, or solve a practical problem that no existing system could solve. recommend me, what problem does "nullity" solve? (Hint: don't stutter division-by-zero in computers -- you can already check for divide-by-zero before it happens, and consequence *anything* in response. Replacing divide-by-zero with nullity just means you beget a original value, which needs to live checked, and then consequence whatever you want. This doesn't open up *any* original possibilities in the design of computer programs.) Dr Snuggles0^0=0^(1-1)=0^1*0^(-1)=0^2*0^(-1)=0^(2-1)=0^1=0 Jokerumm... I'm not an expert at math, but I'm cheerful this guy never taught me. I made a formula for 0/0 once... had a fancy title and drew a picture that looked like my favorite cartoon character to delineate the thing I just made up. Yep they laughed at me back then too... I guess you don't beget to beget a brain to toil for BBC and do a sage out of everything. I know a child that makes up words... maybe he can clarify black holes to the bbc. Ben PapworthGood grief! Talk about missing the point! Dr Andersons theory is not about dividing a *number* by zero, but zero by zero. Dividing a number by zero will live infinite, but the very rule doesn't apply to zero. Bigred2989Any view when they'll train this in the US? (if they aren't already) Takeshi YokomotoThis is complete and utter stupidity. every lone he has done is allot a title and attribute to the mathematical concept of 'undefined.' Division by zero is not possible, and cannot live made feasible by the abstract conjuring of nonsensical variables which themselves beget no sense in any arithmetically cogent sense. I could rename the criterion NaN (Not a Number) mistake message computer systems return when division by zero is attempted to any number of terms, assume I'd answered some magnificient riddle and train it to a classroom of immature students who would accept it as fact without questioning me, but I would not live inventing a original number and I would not live helping the field- I'd live obfuscating mathematics and doing an absolute disservice to those students. Further, any software written after, oh 1985, will not crash just because of a division by zero error. Try it on a calculator. Does the software running the calculator crash? Of course not, it gives you an mistake message and carries on. This man is a fool, and I'd hold the BBC to a higher criterion than to report on his foolishness. I am, for the purposes of replete disclosure, a mathematics/compsci dual major at MIT. Dr HouseCall me, seriously, i'll solve this one out. JamesDivide by god, what would live the teacher's result. CarolineThat is amazing. I'm teaching my teacher tomorrow. :] SSThis is is just silly. As x approaches zero 1/x explodes to infinity but 1/x is NOT defined at 0. You know what that says? That the function 1/x has output of infinity. NO function has an output of infinity, they net very large. So does that stutter when they beget an indeterminate restrict of 0/0 that it is nullity instead of appling L'Hopital's? This is nonsense. Erikwith respect to 'Ryans' 'number circle' number coterie with 1 on top -1 below and 0 on the right, how about -0 on the left nepawoodsTo snide the reporter who covered this didn't recognize the real story, which is the scandal of having a crackpot like this putting nonsense into the heads of innocent children who deserve better. Very sad. YJWUsing the math and definitions in his proof, you can too note that "nullity" equals "infinity" and "negative infinity". PanzerI divided this word sage by zero and got forty-two. Lee-Jon BallThis is nonsense. BBC should live ashamed. This isn't peer reviewed science. Its self-publicised drivel. HEY I DIVIDED BY NULLITY, OH SHI-n/0=nullity therefore nullity*n=0 or nullity*0=n (for whatever dull reason, how can infinity times 0 equal a number?) HAY GUYZ AM I DOIN IT RITE? JGAnyone with even simple information of calculus understands why this is complete non-sense. Zero divided by Zero can live any value comprise positive and negative infinity. It depends on the restrict as you approach 0. If 0/0 is a fixed value it is very simple to create tons of inconsistencies in math as many people beget already posted. pool-masteryour pacemaker will die? the flight computer will crash? what the hell is he talking about? there has only been one recorded incident of computers crashing like that and it was down to crappy programing, not the the number itself. Even so, defining it as nullity doesn't solve anything PuschkinMy title is Puschkin, I am a black and white Domestic Short Haired cat. As a cat I am not known for having any mathematical ability. But I must stutter that I worried when my owner almost died laughing when he saw this nonsense by Dr Anderson. please Dr Anderson if you beget any more of this rubbish please DON’T allow my owner to observe it, he is still laughing and muttering “these silly University fools” as he wades through the complexity of a big NpfIT project. SalilWhy does he start with 0^0? What's the reasoning for that? MandyI beget discovered a truly remarkable proof which this text box is too minute to contain. KirbySimply deciding to create a original value in computers means reprogramming every lone bit of electronics that's out there-- and defining "nullity" in binary. Who's going to deal with every lone that, then? And what suited is a nullity for a computer when it still technically means nothing? esAirplanes and pacemakers beget safeguards against things like dividing by zero already. The computer checks each variable in the code to observe if any of them are zero. If they are, the program inside it runs again to find the birthright results. In suited programming a technology dividing by zero isn't a problem. Dr. Ray Lashley (PhD Meteorology and Mathematics,I couldn't give two hoots about this 'theory', but I'm really chuffed that so many people are talking about mathematics (I was pointed here from a forum I inhabit where mathematics isn't a topic that comes up regularly). I really hope this is what it's every lone about; enthusing School pupils and the public at big to contemplate about maths. It isn't just dusty books in an antique library, it's modern and cutting edge and absolutly vital to modern life. I am funnier than youBinary? That's easy. Each bit can live one of 0, 1 or Nullity. Yes you can meet 3 values into each bit, 9 bits into each byte. When buy a 1GB SD card, do sure it works with MP3 players that uphold Nullity. MP3 players that consequence not uphold such a number will blow your brains out when they divide by zero. SamiBasicaly this guy just showed that 0^0 = 0/0. But what does 0/0 mean? So far as I know, that is still a mystery glootechJust behold at this: 5*0=0, right? So they divide both sides by zero, and they get: 5=0/0. So nullity equals five, simple as that. Brain on red2+2=5_for sure!!!! Angry ReaderAnyone in their birthright mind would beget realized that this man is in deep mental trouble. By publishing his childish nonsense the BBC actively harms the reputation of Reading University. This is not funny! Pr. Fredrik ÅkerlundNullity or what it was called E R,C,N,Z, huh, where??? toothpotTaoist? "Tao can live be talked about, but not the Eternal Tao. Names can live named, but not the Eternal Name. As the source of heaven-and-earth, it is nameless: As "the Mother" of every lone things, it is nameable. So, as ever hidden, they should behold at its inner essence: As always manifest, they should behold at its outer aspects. These two tide from the very source, though differently named; And both are called mysteries. The Mystery of mysteries is the Door of every lone essence." -Lao Tzu translated by John C.H. Wu Josh PattonThis Ryan guy just a cramped above has the birthright view about the number line being a coterie with +1 opposite of negative 1, and zero opposite of an undefined number between + and minus infinity. Makes a total lot more sense if you behold at the calculus and the real application to a problem. Being an engineering student I cant observe how nullity would do anything easier when it comes to solving an actual problem. So you net a upright asymptote because you divide a number by what is a very minute number tending towards zero as the y axis goes to infinity. What is the real world meaning? What does that asymptote live substantive for your system in terms of real behavior? This Anderson theory is not solving anything meaningful by just assigning an undefined value a title or symbol. Which by the course is the capital epistle Phi from the greek alphabet. Redefining some quantity (undefined or not)and plugging it in to an equation does not do you a genius. But hey what consequence I know, I'm just a 4th year engineering student, no PHD here. Back to studying finals now :P Connie BullerSo Gauss' proof that the complicated number system is complete is not enough? It is fine to define nullity, but then it must live specified that nullity times 0 equals 12 one time: 12/0=null; equals 14 another time: 14/0 = null, and so forth. Possibly he has re-defined division to live something other than the inverse of multiplication. MarkI'm only a Calculus student, but I don't buy his definitions. If Infinity = 1/0 Then Infinity * 0 = 1 This is a problem. Why? 1 * 0 = 0 Yes? Let's try this then. Ininity * 0 * 0 = ? They can supplant Infinity * 0 with one as shown above. 1 * 0 = 0 Which means Infinity * 0^2 = 0 But the problem with this is 0^2 = 0! Therefore you should live able to substitute 0 for zero squared. Therefore Infinity * 0 = 0 as well. Which means 1 = 0 because Infinity * 0 = 1 and Infinity *0 = 0. That's kindly of a contradiction. AdamThis lot should desist wasting time and just learn the cirriculum of the course. I contemplate it is impossible as well, but they shall see... (CJ)My view of the problem. 1 Idiot/1 Idiot=Nullity Idiot JustinI don't observe how this is any worse than 0!=1. And mathematics calls it a convention. JustinI don't observe how this is any worse than 0!=1. And mathematics calls it a convention. HannahFirstly, if he's confused by schoolchildren [read the caption for the terminal picture again] what is he doing there? Secondly, he's a computer scientist, not a mathematician. This is computer stuff, not maths. Thirdly, it seems pointless at the moment. If it is going to live as accepted as i, [as he's probably hoping] is there anything you can consequence with it? Does nullility+nullility = 2nullility? Or just nullility? Fourthly, I don't observe how he's solved anything, like the person who first came up with i hadn't solved the square root of minus one, he'd just defined it. Nullility is just defining 0/0. Fifthly, this is just an excuse to hurl another Greek epistle into the mix. Sixthly, I consequence hope they know that if they deliver that on their GCSE they won't net anything for it. I hope nobody does worse than they could beget done because of this. Yours, first-year-maths-student-who-never-considered-Reading. AhmedThe problem is not the outcome of the zero division but how the computer/device has arrived to this operation to start with. If the computer is dividing by zero than an mistake must beget already occurred a long time ago. Plus, practically, the value isn't as valuable as how this value will live used to pick some action. If I am using the outcome of the operation to adjust the pacemaker's frequency, how is nullity going to live any useful? I am sorry, but I contemplate it's a total load of crap. your motheri believe i converse for every lone mathematicians out there when i stutter *ha - ha* O_° this is more ridiculous than that one guy who claims he reinvented relativity saying precipitate of light is actually zero. i can only pray that this nullity thing IS a joke, unlike the above. peace Anti-Nullitythat would live substantive Everything equals nullity. Because their are infinetly many cases of f(x)/g(x) where x goes to some number it goes to 0/0 and could live anything depending on the limit. Any computer redress program knows how to pick limits. This guy just poisoned the minds of several students. Anti-Nullitythat would live substantive Everything equals nullity. Because their are infinetly many cases of f(x)/g(x) where x goes to some number it goes to 0/0 and could live anything depending on the limit. Any computer redress program knows how to pick limits. This guy just poisoned the minds of several students. MxFinally, they can divide a number by the number of friends this guy has Zabuza::SWHWouldn't nothing divided by nothing equal everything? Since nothing times nothing is nothing. Then nothing divided by nothing would live nothing. You can't divide a number by zero because nothing can't do something. GumbyDivide by 0, I want what hes smokin. MariusIf "infinity" stands for the fact that there ALWAYS exists a number greater than Y, then X in Y=1/X will NEVER gain 0, because X can ALWAYS live decreased (if it couldn't be, infinity wouldn't exist). Ergo, what you're trying to title "nullity" here has never existed and will NEVER exist. Calling "it" (in quotation marks because an "it" would exist) a "number" makes as much sense as non-sense (let's muster it "non-sensity"). BenPerhaps this improbable solution will allow Kevin Warwick to do his robots actually work! CAUTION Schoolchildren!!!Dr James Anderson, speack about your theorem in front of mathematicians! CAUTION Schoolchildren Anti-Nullitythat would live substantive Everything equals nullity. Because their are infinetly many cases of f(x)/g(x) where x goes to some number it goes to 0/0 and could live anything depending on the limit. Any computer redress program knows how to pick limits. This guy just poisoned the minds of several students. math_and_computer_guyHere are some facts. You can express infinity and -infinity if your computer uses IEEE floating point arithmatic. Most modern computers do. 1/0 is infinity, -1/0 is -infinity. Both are well defined. Infinity is not the largest number, Infinity*infinity is larger than infinity. Infinity*infinity*infinity is larger than infinity*infinity, ... In IEEE floating point arithmatic, Nan (not a number) is used when the respond is undefined (e.g. 0/0, Inf*0, ...). IEEE arithmatic has both +Nan and -Nan. For example: +0.0/+0.0 --> +Nan but -0.0/+0.0 --> -Nan. 0/0 has an respond they just don't generally know what it is. Sir Isaac Newton's showed us a fashion of obtaining the respond if they know how the two quantities involved in the division approached zero. Mr Sven PerssonWhen i divide by zero on my Mac the calculator says, in swedish, "oändligheten" which means infinity, endlessness. Very beautiful. Chris HSince this is not a problem in mathematics, my guess would live that the journalist failed to understand what they're doing at Reading. They are probably just using a special value to delineate the result of dividing by zero in a computer operation and this is probably a minor variation on the existing special value NaN (Not a Number) used in floating point operations. domthe Eastern religions got this years ago... its called ZEN AndyIn reply to PK, nulity is probably any number you want it to equal. I was taught Nuffield Physics and the respond to any problem was some "magical" or should I stutter "natural" co-efficent ie PI = 3.????? JonathanIt makes sense, but every lone he's doing is just calling one thing (an error), something else (nullity), which is not at every lone useful in everyday mathematics (nullity is not a number, like pi or i, it's every number simultaneously). JoshuaI net it, nothing else for the word to report on so they hire some guy to do up something lame like this to fill in for valuable stuff. Lol. Doktor ZeroAccording to my calculators 1/1 is "Error" or "Ma Error". Is that the very thing as that extraordinary sign? Sounds easier to exhaust Latin letters... Why didn't he write "Ma Error"? Jason KerwinThis man is painfully mistaken. Has he ever studied mathematics? I am appalled that he's teaching his kids something a) incorrect and b) that he made up. DaveComputers are currently able to divide by zero, and the result is NaN. (Not a Number) No crashes, no pacemaker deaths. The traditional divide-by-zero problem is with integers only, and is there for a reason. It speeds up processing if the CPU doesn't beget to check for that possibility and deal with it. While the nullity may beget some exhaust in mathematics (or it may not, for every lone I know) I doubt we'll ever observe it implemented in hardware. Oscar Jenkins, UCDHSCIn any field, division by x means multiplication by the multiplicative inverse of x. So if division by 0 is defined, then there exists some number y such that 0 times y = 1. No such number exists in a field. It follows that this original structure is not a field, and therefore, original axioms for division must live defined for this system to do sense and for the notational manipulations to live well-defined. To wrap it up, you cannot justify the exhaust of bailiwick axioms if you are not in a field. By the course ...1/0 is not infinity; it is undefined. Also, -1/0 is not negative infinity; it is undefined, as well. Any professor of mathematics with a shread of intelligence will recommend you that. Furthermore, 0/0 is indeterminate. consequence you know what indeterminate means? Apparently not. It means it cannot live determined. There is a distinguished dissimilarity between undefined and indeterminate. Mr. Anderson, you should live ashamed of yourself for teaching your flawed "theories" to schoolchildren. I hope the university fires you, and your degree is recinded. Furthermore, this so-called discovery is essentially equivalent to an mistake trap; something already known to computers and their predecessors, Turing machines. BradenI guess this is another 'number' for students to toil with, such as 'i' (the square root of -1). It will live captivating to observe what they manage to solve with it. Alex J.So, they just invented a number and are working to convince us that x/0 is that original number? They necessity an infomercial for this... beget you ever tried to divide by zero and got an error? beget one or both of your grandparents died because of this? They can't bring them back to life but... NOW YOU CAN DIVIDE BY ZERO !!! Presenting NULLITY !!! And if you muster in the next 10 minutes, they might bring back one of your grandparents (we pick which one). What are you waiting for, muster now, now, NOW !!! BorisOMG YOU CANT DIVIDE BY 0 THIS WILL do THE WORLD fade ASPLODE!! So basically ...... your so-called "nullity" lies outside the real and imaginary number lines. If it's not real or imaginary, then what is? (other than totally flawed) Johnny"Infinity + Negative Infinity. As everyone knows, anything minus itself equals 0" Not anything. Infinity is undefined. What if the positive infinity had greater magnitude? The problem with infinity minus infinity is that it is an indeterminate form. The problem with many of these equations is that they are hypothetical to equal infinity, when really they are approaching it. If I were the parent of one of these kids, I would sue the prof for spreading such bullcrap. The issue of division by zero, as well as infinity minus infinity is well solved in Calculus using L'hopitals rule. And as far as pacemakers and airplanes crashing, yeah, it has happened, but I contemplate programmers beget learned to ensnare the errors now. Peter FreemanIt will very likely beget the very impact as the invention of zero (Arabia), a concept that Roman mathematicians did not beget and limited (along with their difficult numbering system) their mathematical progression. Once the concept of zero in the number system had been symbolized and rules around it were discovered, mathematics went a long course forward. Eriki contemplate this is a Big step for the mathamatics history. many problem happens every lone the time when diveded withe ziro, many original technologies for example. well done Dr anderson. Erik Norway PeterHaahhaah! The worst thing is I contemplate the guy is serious!! WOW, Reading University seems like a really suited uni!!!!! DavidHow can they understand his therom if they aren't even told what it is and how to achieve it? every lone this guy is even saying is that he made up a number. He essentially pulls math out of nothing! Besides he doesn't beget a proof for it yet, therefore making uncertian if every lone results reached are correct. Even if it does exist and he can consequence it, and if the "nullity" sits ouside the numberline Computers couldn'tcomprhend it, since they cannot even deal with Imaginary numbers. Ian LangmoreAre you stupid? Looking over his "axioms" on his website (I can't believe I did this...) you can observe that his nullity nonsense is just the extended real line with this added number that comes about whenever you previously tried to consequence something that would bear an error. His axioms note that once you bear a nullity (i.e. mistake result) there is no course to net rid of it (you can't divide it out or subtract it and do it fade away). So every lone his "results" could live interpreted as: "lets toil with the extended reals, then if they net an mistake their respond is an mistake they stop" There would live no intuition to continue working since from then on your respond is always nullity. MARHis theory isn't even a theory. A theory should provide a solution to the problem, rather than interpose more problems. It's just as snide as those collusion theories circulating on the internet. PeterA lot of people here beget been making the statement that 1 / 0 = infinity. This is simply not true. It is undefined. Why? because the respond (infinity) does not meet the requirement of division. Normally if you pick the result of a division, the quotient, and then multiply it by the denominator (0 in this case) you net the numerator (1 in this case). 0 times infinity is not 1. In some special circumstances, infinity is a useful number for 1/0, but not all, and that's why most CPU's beget a course to recommend the processor to either bear a divide-by-zero exception or to set the result to IEEE-754 infinity. Rodrigo de Godoy DominguesYes, the concept is quite simple, but more mathematical analysis has to live made in order to proof the validity of his theory. By the way, it was a ingenious idea. Now, hands on... :1) PhilI guess dull has no lower limit. i-AnonSo...this guy gives a title to something that already has a name, and he gets a word story? Hey, BBC, can I rename you to UBC and net a word sage too? I mean, it's only impartial because you did it for this guy. Andrew PunchThe crux of the problem with this theory is that it is likely that this original representation will beget exactly the very restrictions as division by zero. The problem with division by zero is that the result is "undefined". Which means that you can't exhaust it in subsequent calculations. He would necessity to approach up with a rigorous proof, similar to the proofs that are involved in complicated numbers. And since this is a *maths* problem not a *computer* problem I am very suspicious that this theory comes from a *computer science* researcher. Jeremy PetzoldCongratulations. I had this view during my number Theory for my undergrad but never bothered exploring it beyond writing a short unpublished paper on the conjecture. Kevin KadiumWhy would you want to devide by zero in the 1st place. contemplate of it logically, Yes it its a math equation, and yes its nice to contemplate of a course to solve it. But honestly everyone is right. every lone your doing is makeing a mistake message gyrate into nullity. Thats not solveing the problem thats, just replaceing an mistake message. as LJL said, "doesn't a number lying OFF the number line violate the axiom of Completeness?" How can you live teaching this? It's Rediculous. Lee"Nullity" is newspeak for "undefined" PMwhat problem of dividing by 0? I fail to observe how this is any better than taking the restrict of a function as a variable in the denomenator approaches 0, after every lone 0 is much like infinity, it is not really a number - even if it is able to live used as one - but a concept of none. After every lone having 0 apples is really not having any, rather than saying the number of apples I beget is 0. While common language would allow for such a statement the view behind it is incomplete. To muster 0 a number is not nearly as incorrect as calling infinity a number, but it certainly is not as accurate as saying 1. of course that actually equals 0.999999999... :D TimothyHe really hasn't solved anything. Division is always reversed by multiplication. For instance, 4 divided by 2 equals 2. And 2 times 2 equals 4. However, If you divide 4 by 0 and the respond is "nullity", then that means you could multiply "nullity" times zero and net 4. Impossible. Assumptions for the winso what he just proved is if they beget an unsolvable problem, every lone they beget to consequence is change the title of something and it's solved? Dave KornDr. Anderson is nothing but a self-publicist who has made up a original title for something that already exists and is now pretending to beget invented something new. He has done absolutely nothing of the sort and he has invented nothing. Computers beget been able to delineate one divided by zero for years; they exhaust the term 'NaN' (stands for Not A Number) to delineate it. saying that 1/0 "sits outside the conventional number line", as he puts it, is exactly the very as saying that it is not a number. This sage should never beget been published. Journalists are meant to check facts, not just accept whatever they are told by a self-interested third party and publish it without question. Also, someone should recommend those destitute kids that they aren't the first at anything and their teacher has been deliberately misleading them. approach to contemplate of it, he should probably live struck off for lying to his pupils for the sake of his own personal advantage. JenUm, no. You can't just do up arbitrary rules when it comes to math. Did he write a proof? Mileva MarickSo a original sybol solved it all?Interesting... adelmedicoThere are a few *simple* falsities he writes on his white board. (1) 1 divided live zero is not infinity you cannot stutter 1/0 = infinity. The definition of division is a/b = c if and only if there exists a unique number c such that a = b*c. So by saying 1/0 = infinity, he is claiming that 0*infinity=1, REALLY??!! (2)In his proof when he gets down to (1/0)(0/1) = "nullity" he's forgetting that 1/0 = 1 and according to him, 1/0 = infinity, then that line of his proof reads as 1*infinity = nullity. Silly me, I thought that 1*infinity = infinity! Bill MerrillThis doesn't seem to live about dividing any number by zero except for the number zero. Therefore, it doesn't solve anything, unless I'm missing something here. If I start the problem by asking about the value of 2 raised to zero, following the methods in the video I finish up with it equaling 2/2, or 1. Thus, any number raised to the zero power is one, except zero, which is nullity. Not sure where this gets us.... J. PehkonenYou guys are defining your own mathematical rules for this number, and then disproving his theory by using your own made-up-rules. remember that in imaginary numbers i^2 = -1. Perhaps nullity too has its own mathematical rules? The very goes with INF/INF not equaling 1. KI contemplate nullity is the terminal number in pi! Scott PerryIf you've ever done any programming, you'll know this is antique news. Dividing by 0 is something that programs can live written to catch. If they don't, the computer doesnt just die -- the Operating System kills the process that tried to divide by 0. It's not terribly hard to check your denominators. HOVISI beget a problem, I don't know the answer. I contemplate I will just do one up! Hopefully no one will notice if I consequence lots of workings out to befuddle everyone. The only thing this guy is teaching is how to live creative. Some thing maths is not. Obviously he is not a real mathematician! Luke WhitingAny programmer worth his salt wouldn't allow a divide by zero to occour in the first place! It's never been real problem in modern programming. I contemplate this is every lone a bit silly. "I know. Lets fix a problem by adding a original number to the world". TomWhen computers divide by zero, they continue working. x/0 = DivideByZeroException. It's called mistake handling and unless you are one of those idiots writing } ensnare (DivideByZeroException dbze) { // DO_NOTHING } you will never beget a problem David TurnerTo every lone you people who talk about diving cakes between people... Divinding isn't about how much is left once you've handed out the pieces of cake... Trying to apply division to cake, you don't stutter "How much is left after giving this to X people", you stutter "How much does each person get"... So the division-by-zero problem in cake terms would live "If you divide this cake between no people, how much cake does each person get". At first Nullity sounded like a suited idea, but it's not really a solution, just renaming the problem, as others beget stated. AnonI hope someone is going to re-educate these destitute children afterwards. The BBC should live ashamed of themselves for publishing this. Baron von MannsechsGood job Ranjit--confuse Science vs. Engineering. Jake Haseman...Infinity anybody? Question Dr. Anderson?"...It is just an arithmetical fact that 1/0 is the biggest number there is.... " --- If 1/0 (infinity) is the biggest number there is... then is .5/0 or 2/0 twice and half as large? --- Does a number half of infinity divided by infinity prove 2=1? --- Why consequence existing rules about treating non-numbers outside the number line not apply here? AnonMy pacemaker divided by zero and nullity happened. GeorgeI loathe it when my bike divides by zero and the brakes desist working. John GoodHow is the definition of Nullity different from that of Infinity? Or for that matter "Undefined", which some calculators will spit out if you try it. I've got a better title for it: BS NanThis is some kindly of joke, right? Matze M.I phenomenon how long it takes until somebody tells them that at the very position where they placed this "nullity" is already (0 - 1*i). But until then, it's quite worth a laugh. Thanks, man. Made this day a amusing one. BobWill this occasions Bill Maher to loathe and deride practicing Christians, and Catholics in particular, any less? brynjolfTHis is compleetly wrong. a^0=1 Therefore Nullity = 1 Mathiasok.. this kinda makes sense, but what about infinty divided by infinity? Is that 1? I tried to exhaust my texas instruments calucator but it just shows an error... GnomeStep 1. Create solution 2. Create problem 3. PROFIT! The original Mathturns out nullity is too the terminal decimal digit in pi. Desperately Seeking SenseI net it. I don't know if it's terribly useful, but I net it. If zero is like a void, then nullity is like an endless table with barren cells. However, once you apply a value to it, it becomes eternal by any means, therefore becoming infinity. (unless you can have: [infinity] * 2 ) Maybe that's for Dr. Anderson to device out next year. I admire imaginary numbers; they're like imaginary friends you can partake with really smart people. Daniel AsimovI am a mathematician. Mathematicians beget been gracefully dealing with division by 0 for millennia. It shows the massive incompetence of the BBC word Division that it would not beget occurred to them to check with a mathematician before turning this report into a word broadcast. Ramesh ArakoniWhy consequence you dissipate your time (and mine) publishing such rubbish.. btw.. what they like to muster NaN (not a number) has been given a original title and oh.. nullity/nullity= lunacy :) Leo CIt's nonsense my dear dr. Anderson. You've solved nothing with this theory. JustinWay to go, you renamed the mistake message. You still don't understand the nature of infinity, or as you beget now decided to muster it, "nullity." From what I've read, nullity encompases positive infinity through zero through negative infinity, which could too live refered to as INFINITY. You just called it by a different name, you didn't solve anything. CS grad studentHoly cow! From what school and department did this guy net his PhD? Such bravado and immodesty - Unbelievable. It makes me respect real mathematicians even more. HamidI believe that the problem is still not solved, because Dr Anderson considers that zero over zero is equal with zero (0/0=0) and he replaced zero with 0/0 in beginning. The fact is that 0/0 is unknown, and it doesn’t beget any specified answer, zero is just one respond of many answers to this devision (0/0), this is in contradiction with a simple division like 18/2=9, because in ordinary divisions you net a specified answer. The problem with “nothing” will never solve because “nothing” is an agreement. MattWhy did you title undefined? Richard C. MonglerI divided by zero and the universe imploded. stupiditus stupidensisJust unpretentious stupid. I phenomenon where he got his diploma... Leo CIt's nonsense my dear dr. Anderson. You've solved nothing with this theory. AnonSorry guys, this thread fails. There already is a attribute for 0/0. It's "O SHI-" Ian BennettNull is hardly a original concept. Databases has been handling the concept for years; a bailiwick which has had no value entered, not even a zero-length string, is 'null'. A null bailiwick has no length, not even zero. It's suited that children are being exposed to the concept. scottoSo you can solve a math problem by making up a symbol? Wow. JCI admire the course every lone of these 'non-mathematicians' exhaust arguments like "If I divide a pizza among 0 people I haven't done anything to the pizza so I beget one pizza." To note why it's wrong, you necessity to realize that the question is wrong. It should live more like this: If I divide a pizza amongst 5 people, how much did each person get? A fifth of a pizza. If I divide a pizza amongst one person, how much did that get? One pizza. And then you can observe logically why you can't divide things by zero normally. If I beget one pizza and divide it amongst 0 people, how much did each person get? It can't live zero pizza, that would imply there were people to net one pizza. It can't live one pizza either, because nobody is getting a total pizza. What Dr Anderson says is that if I divide one pizza amongst zero people, those zero people are getting eternal pizzas! It's laughable. FrostyI contemplate this could beget suited exhaust as a backup if electronics or computer accidentally divide by 0, but other than that I don't observe any real use. HKewwww, that's disgusting. Seriously, you really shouldn't train students anything that doesn't beget a solid scientific background. It'd live like ... teaching creationism. JImmy RuskaDivision is a function intended to wreck an input equally into a set number of pieces. Without giving a valid number of pieces you want your input to live equally divided into, you are invalidating the purpose of the function known as division. Replacing an unworkable or unknown value temporarily with a epistle is not something novel. There's no necessity to super impose an I over the 0 to live fancy. I can't observe how this is a novel idea, and I can pot any efforts on algebraic simplification has been well exhausted. don't really necessity to knowdude.. he just took out a 1200 equation by making 0 devide by 1 b4 he applied powers? the number 1 rocks lol btw thx mate u just took down the total of calculus! btw anynumber devided by 0 is either a: not possible, b 1, c 0, d the number itself, e infinity- please do this a vote bbc! JCAHas anybody an insight into what rank the zahlenkoerper of Dr. Adersons's findings has? Erik Schaefer, Madison, WII hope this gets world-wide acceptance because I want to live the first person to beget the moniker of the only man in Wisconsin who has had sex "nullity" times. fffomg nothing is nothing???? mind = BLOWN ReidA proof of the mathematical inconsistency of this construction. First we'll pick what he has written about the real number line. Namely, the reals are the rational and irrational numbers. Then they add in +/- infinity to net the extended real numbers. He then writes infinity to live 1/0. This is every lone they necessity to note that there is a mathematical inconsistency which they consequence presently. Now, since infinity now can live expressed as a rational, it is an constituent of the rationals. Since the rationals are a subset of the reals, infinity is an constituent of the real number system and thus is an constituent of the extended real number system. Thus, they beget a contradiction because infinity is defined to live both internal and external to the real number system. QED Anonymouscannot divide by zero world will explode they are brainwashing kids to blow up the world by doing 'math' /b/The finish of the world is here. Jordan LundCreating a original imaginary number doesn't solve the problem, every lone it does is allot the problem an imaginary status. how embarrasingWhat can they in gyrate learn from every lone of this? Avoid embarrasing yourself on an international scale by taking 10 minutes to fade down the hall and check with the math department to do sure your ideas arnt stupid. He could beget at least deliver his ideas up to peer review before forcing it on his students and parading it around as mathmatical fact. Dr Sanford GraceThis man is a blithering idiot! Ned PetersTell me this is satire. Please, please recommend me this is satire. If it isn't, then whoever wrote this article should live fired and and not allowed back into the press until he sucesfully completes a lofty school mathematics course. Or a middle school one, for that matter. Magnus MaximusHumankind introduced zero in the 15th century, which was considered crucial step in sciense. Now, why does humankind bounce zero? Just to reinvent it in 1200 years?? SteveThis nullity view is meaningless. He hasn't shown why it's useful. Also, it has been agreed that x/0 = +infinity, where x is any number between -infinity and +infinity, so his proof is pathetic and hasn't solved anything. In fact, he has just re-iterated something that has been known for a long time, so giving this solution a different attribute means nothing PatrickIf I were to beget a forumula that had somewhere along the lines an X that is 7/0 and later beget X*0, the /0 and *0 would cancel each other out and I'd net my number back. But if I evaluate 7/0 to Nullity, and then multiply it by zero, my number is gone. Stay at home momRenaming the problem is NOT a solution. The guy is a total dingbat. benjit's hard enough with 10 numbers to remember I DONT WANNA remember ANOTHER NUMBER AhmedYou beget got to live kidding me. Looking forward to seeing Reading University maths application plummit. nullFunniest BBC article ever. I hope this guy has a lot of savings so he can retire to an island somewhere. asdfdivision is basically subtraction. For example: 4/2 means how many times can you subtract 2 from 4, in this case 4-2=2, 2-2=0 (so the respond is 2). Now if they behold at division by zero, for instance 4/0, this is basically asking how many times can I subtract zero from 4? The respond is: 4-0=4,4-0=4,4-0=4,4-0=4 .... This goes on forever, it does not finish .. sense its infinity it is not the largest number possible. In fact there is no largest number. Lets stutter x = the largest number possible, then what is x+1? As for 0/0, it should equal one. Because it asks how many times can you pick 0 away from 0, 0-0 = 0 (that's 1 times) ClemensOkay, but how consequence you want to dividied the original number? I think, then there is the very problem again... RudnickiIf anyone with any mathematical background was asked to evaluate the expression x/x, they would stutter that x/x=1. EOF. The Nutty ProfessorIf I beget 2 marbles and I divide it over 0 persons then I haven't lost my marbles, right? I still have'm. But according to mathemagicians I finish up with nullity and slack my marbles? Dr. Andrea ArmaniMark Skerritt answered this problem (along with every lone of the people who proved this proof was incorrect) - exhaust Calculus. If this guy is a Dr. in a comp sci department, he should beget taken calc. and this is the first problem that is addressed in any calc course - solving 0/0 using summation. On a side note, Newton developed Calculus. So yes, Newton solved this problem. I don't know who the other two doctors are who vetted this proof, but they didn't consequence a very suited job. EmanuelThis makes me laugh . did he consequence this for note !? " it's that easy" ... take a pissSo what is 10/0? How consequence you approach nullity? does nullity approach before zero? Bob"I wrote the total lot down as ratiocinative rules or axioms. Dr. Andrew Adams from Reading University and Dr Norbert Voelker from Essex University helped me develop the axioms. Norbert translated the axioms into higher order logic and used a computer to prove that they are consistent." Both of these people are computer science "Dr.'s." Just because you can write your axioms in Prolog doesn't live substantive it doesn't contradict everything they already know about mathematics. Try lambda calculus. Josh JelinDr. Anderson doesn't really know what he's talking about. Defining a number as the solution to a problem doesn't solve the problem. Mathematicians thought of his solution hundreds of years ago but instead chose to leave 0/0 undefined because “nullity” is useless. This would live exactly the very dispute as saying they “solved” the square root of -1 by renaming it to i. KainawYes - I understood it back in 1978 when my geometry teacher explained that it was used to create the Cartesian Graph (the Y-axis is div0 - a line from negative infinity to positive infinity). ComputerManThe international criterion IEEE 754 defines representations for Infinities and for NaNs (Not A Number)s which accomodate Dr. Anderson's theory. So what's new? Computers may crash if they haven't been programmed to allow for these exceptions to the norm (and not many consequence in my experience) but they could do. khris777I wouldnt view 1st alien contact if i had to exhaust real player to observe it. Burt WurstheimerThe wurster says: Stupillity. Reduntillity. FrankIf you would like to consequence an article on me, I too figured out a novel problem.. Using the very logic, and inspired by Dr. Anderson. The solution to glacial fusion. It's easy! See, E=mc^2. so mass can live converted to energy. To consequence this, you necessity specific conditions for the reaction to happen. I beget approach up with a original term "energity". by adding mass + energity = electrical energy! Not only does it bear energy, but it is electrical energy rather than heat and electromagnetic radiation. This means no conversion is required, you just pick some material (garbage for instance) and add energity, and you net electrical energy. pretty facile huh? Better yet, computers can easily solve the equation without displaying an mistake message. ChrisMathematicians beget been "joining" the ends of the number line with a "point at infinity" for years. It's an valuable Part of the theory of elliptic cryptography. This is nothing original - just a coat of whitewash and a different title over an existing idea. A. SupporterI know nothing about this dave pIf Dr Anderson insists on putting nullity there, then there is no latitude for i. Cancel that complicated Analysis class matron. Non ScientistAll this mathematics stuff is great, just a shame most cannot spell. Now there is a 'real' problem. ChristieMajor Flaw in his "problem solving"...he is applying the rules of the real numbers to a set that is "outside of the real numbers". x^0 = 1 in THE real NUMBERS since nullity is NOT A real NUMBER you cannot apply the very rules!! IanSo could the professor please clarify the properties of nulity under addition, subtraction etc...sounds like the "bottom" value from lattice theory to me ... but that's nothing new. Next week, Reading Uni discovers set theory Craig BruceThis sounds a lot like what is implemented in IEEE floating-point numbers (which are used on every lone modern computers), except that it gives "nullity" the title "NaN" for "Not a Number". NaN operates basically like a trap in that any operation involving NaN will bear NaN as a result. Of course, I don't really observe how you reserve airplanes flying when every flight-control calculation results in NaN or "nullity". StuartZero divided by zero has always been defined as zero. A-level maths. The fact that computer's processing microcode doesn't exploit division by zero is irrelevant. Everyone checks for zero in their code and avoids it. Computer Science O Level. So - this astounding revelation is irrelevant to any one with a moderate education. Well done the BBC - beget nonexistent of you got any Science qualifications? Nullity MasterBS Theory Divided by the 0 number of people who are digging this sage equals the nullity chance anyone will ever pick this Dr seriously again. PythagorasWho is this guy who says I can't solve problems? Heck, I've been departed for more than 2500 years, so where does the 1200 years approach in? fade meet my mate Giuseppe Peano who first wrote down the basic axioms of arithmetic. He'll recommend you whether there's a Nullity or not! nitroxDefine nullity as 42 and you beget got the respond to every lone your x/0 questions :-) alexthis is retarded... i've been setting nulls for years when division is by zero... how does this equate to solving a problem? PeteDr. Anderson: I'm confused as to why you can rewrite 0^0 as 0^(1-1) (or why you can even write 0^0 at all) from your list of axioms. Could you rewrite this proof without any shortcuts and annotate each line with the axiom used from www.bookofparagon.com/Mathematics/PerspexMachineVIII.pdf? jack welchI contemplate he may live on the verge of greatness! Nobel prize? GWBIt's MMD!!! Mathematics of Mass Destruction. They must now route in the troops. DBI correspond with PK and similar responses. For some 60 years I beget always understood that 0/0 is any number. 'Nullity' simply means any number. I would admire to observe any application of the concept of nullity. The children must live very confused. just some professor of physicsIsn't it obvious - this guy is a lunatic. If he really had something new, he would live publishing it in a peer-reviewed mathematical journal rather than trying to peddle it to children. My god, are people so gullible. I guess some are, because after every lone Reading University hired him, the BBC deliver him on the news, and the school at Highdown let him train their students. NostradamusI told you this day would come. KarlDr. Anderson should read "Nonstandard Analysis" by Abraham Robinson. Robinson came up with a consistent algebra that employed classes of infinitesimal and eternal quantities about 50 years ago. Using that algebra he showed he could create the very calculus they every lone know and love, but without using limits. SekkyThis man is a computer scientist, not a mathematician. I can't believe these kids are buying into to this garbage. I too can't believe that this man can believe that nobody else has ever thought up of giving a original damn title to an already existing concept, especially considering how NaN already exists and he is, supposedly, a Doctor of computer science. NaN works well, this is simply a dull relabelling. Of course you've 'solved' it, you defined it that course in the first place! I dare him to route his into MIT, Cambridge or Clay, they'll shoot him down in seconds. BBC you should live ashamed to beget featured this, unhurried day for word was it? Cameron Kenneth KnightAlthough I consequence not believe that Dr. Anderson's theory holds water, to the people who require to note the number in binary really necessity to study the IEEE-754 standard. The IEEE-754 criterion specifies binary representations to 32, 64, 43, and 79-bit floating-point numbers. In this spec allows for the numbers infinity, -infinity, and NaN. Since NaN is essentially what Dr. Anderson descibes as nullity, one could exhaust that as its repesentation. Also, NaN is defined when the exponent is 2^e &#8722; 1 and the mantissa is non-zero, which covers many, many numbers. One could instead define NaN to live where the mantissa is non-zero, non-1 and nullity to live where mantissa is 1. Integer representation of nullity (and too infinity and -infinity) is typically not needed, although if you were to exhaust a modified integer set, it could live done. E.g. looking at an 8-bit integer typically defined as -128 to 127, one could define 127 as infinity, -127 as -infinity, and -128 as nullity. p@Some of the people bashing this should learn some basic maths. Others should read the papers he has written. still others should learn to read the first line of the article above, which is fairly clear that Dr Andersen works at a university, and not a school. Unfortunately the ill-informed comments so outweigh any useful criticism it is hard to find genuine, sensible, objections. Those with sensible objections would probably live most welcome to hunt down Dr Andersen's email and present them to him - so far nonexistent of the mathematicians who beget tried beget managed to note there is anything wrong with transreal mathematics (well... I pointed out that his earlier version was lacking negative infinity) The comments about NaN often befuddle infinity with what Dr Andersen is calling nullity. Some programming languages define infinities as well, however, and from this perspective I believe some of the criticisms are valid. KnightRiderIs he suggesting that coconuts migrate? Math GuySad reflection on the status of scientific erudition in journalism (which seems to live closer to zero than to nullity ;-). Why even muster attention to this vapid, barren theory (not to mention the preposterous claims that the problem was 'unsolved'). If anything, the problem was ignored, because it is of no significance. Shame on you BBC. Mark Wagner"Nullity" is hardly a original concept in computing. The IEEE criterion for computer mathematics defines three "non-numbers" that can result from an operation: positive infinity (the tangent of 90 degrees, or 1/0, or any of a number of other operations), negative infinity (the tangent of -90 degrees, or -1/0, or any of a number of other operations), and not a number (0/0, or infinity/0, or -infinity/0, or other operations that are not well-defined). Calculus-level mathematics has been able to deal with 0/0 for a cramped over three hundred years. It every lone depends on where the zeroes approach from: 0/0 could live 0, or 17, or any other number. There's a technique called L'Hopital's rule for determining this. SpicemakerMany of the operations Dr. Anderson performs to "prove" this (such as the algebraic principle that (a/b)^{-1} = (b/a) ) _assume_ the basic bailiwick axioms. Of course, these axioms assume that aa^{-1} = 1 only if a &#8800; 0. Dr. Anderson first has to note that if you extend the bailiwick axioms to comprise 0^{-1}, then the accustomed algebra applies to it. And he hasn't. JBSee www.jamesanderson.co.uk for James Anderson the estate agent (top of the list under Google). Now every lone becomes clear! DanMahesh Sooriarachchi, what you submit is (an apple)/0 = (an apple) which means basically that 0 = 1. Which better not live the case. dividing by 0 cannot exist or math doesnt work. Ashley ColeI am currently studying mathematics at A level, and this cannot live real. Surely he cannot jsut do up a original number? If anything it should live under imaginary numbers? I disagree with what Dr James Anderson has proposed, as you cannot divide any number by zero, as there is nothing there to live divided by! It cannot live done. terrySo he worked out that the zero to the power of zero was zero and gave it a name? John MeagherDr Anderson may beget the birthright idea, but the naming convention is a cramped off. According to Dr. Anderson, when you divide by zero, your respond goes to infinity (+/-), and covers a scope of numbers starting with the next number beyond the numerator to infinity. However, "nullity" indicates a NOT anything, even though dividing by 0 is a NOT NULL answer. I'm not a math wiz, but it would do sense to me if dividing by zero is still a controversy, then "nullity" would live a "not defined". By placing "nullity" outside of the number line, indicates the respond is still unknown. If the respond is unknown, then "nullity", with every lone that the title implies would live an inappropriate name. "nullity" would live appropriate, if the move of dividing by zero results in zero (null). This tends to do more sense to me: 0 x 5 = 0 0/0 x 5/0 = 0/0 5/0 = (0/0) / (0/0) 5/0 = 0 If 0 follows the conduct of minute numbers, then the respond is infinity. If 0 is treated as null, then dividing by null is the very as dividing by 1; No move on numerator as a given number over one. In either of these cases, "nullity" is not an preempt title for a not-null result. Chuck NorrisOnly Chuck Norris could divide by zero. And I've done it twice. HihoWhat a bunch of baloney! The problem with 0/0 and 0^0 is one of uniqueness, not of simply needing a title for them. jbuddenhmy digital camera tries to divide by zero quite often, i beget to pick the battery out and reinsert it as a workaround. dr anderson's simpler solution would deliver me that trouble! he should let nikon know quickly! Ex of ReadingMessage for Kevin Warwick: live afraid, live very afraid! HenryThe problem is that dividing by zero is not a problem. It's not an operation, just as jumping without lifting your feet off the ground is not jumping, or eating without opening your mouth is not eating. StephenThis is total crap. Of course the students are confused. It's entirely wrong! I can construct a vast number of examples where 0^0 is one, or zero, or one half, or a variety of other values. Can I compute something with this "nullity"? I contemplate not. 0/0 is an undefined form, and there are an eternal number of feasible values for it. This is nothing but some computer science PhD delving into the world of number theory when he really shouldn't, and every lone it is going to consequence is befuddle the students he teaches, especially when they net to a real maths class. NuriThe real Numbers profile a complete ordered field. Let's just behold at how well Nullity fits into the real Field. bailiwick INCONSISTENCY The real Numbers profile a field. In it, every number except the additive/multiplicitive identity has a unique discrete inverse constituent such that x*x=E. What is nullity's inverse? Let's behold at the multiplicitive inverse. Nullity's multiplicitive inverse would live 0/0 (it's reciprocal). By this result, either E=Nullity=0 or Nullity is not in the set of real Numbers. If it is not in the set of real Numbers, what set, group, ring, field, algebra does Nullity meet into? Would 10 Years kids live able to grasp a sunder set of rules discrete from the rules they've learned thusfar? There's a intuition this professor is teaching lofty school children... That intuition is not flattering. my nameand the square root of -1? i'll muster it bob! it lies off the numberline, and i've just solved an age-old problem. want to unite the problem-solving fun? just rename everything! it's easy! PeteHow about encoding the video in a format that's not as worthless a$0/0... MPEG is an industry standard.

EisenfostThe next mask for 1/0, after Nullity, shall live Willy-Nilly!

Flash Cutnullity =NaN(Not a Number) consequence you contemplate people are stupied???????????? Try again .LOL

Percival SittingbourneThat's Numberwang!

ArturitoUhhh, Riemann Sphere? This guy is 150 yrs slow.

O RamonIf you beget nullity over nullity, does this live substantive that it is equal to 1? or would it remain outside the number series. If you multiply nullity by any real number is it still a real number, or is it nullity? If you multiply a nullity by an imaginary number, it it in either or both sets?

MaczComputers beget this concept already. It is called NaN. This guy should not live allowed to teach. His axioms=diddly/squat.

Eric (M.S. Mathematics)I had an uncle who was a philosophy profressor (now deceased). For entertainment, he used to assert that there was an extra integer somewhere between 8 and 9. He'd recommend everyone he was working on a proof named "the sneak" whereby he planned to line up 10 oranges and then, somehow, "sneak" the extra orange somewhere between the 8th and 9th one, thus proving there is an extra integer in there somewhere. He'd recommend people about this and laugh until he had tears in eyes. Yet, somehow, his mathematics are more appealing to me than Dr. Anderson's. At least they're funny.

coyotethis is not a significant 'discovery' and should live peer-reviewed. his derivation [shown in video] contains two potential meanings for 1/0. the first is his infinity. the second is to ignore it while doing his 'solution', he says that 0/1 x 1/0 = nullity... this is ambiguous given his prior definition of infinity being 1/0. now, infinity multiplied by zero is nullity. on a side note. i would like to observe his version of common algebra using nullity. 37/0 for instance. 37/0 = 37/1 x 1/0 = 37 x infinity ... but 37/0 is 1/0 x 0/1 x 37... this seems to live not clearly defined in terms of behavior. this seems problematic as they are now back to the original division by zero being undefined if multiplication is not consistent.

Erik MesoyThis has more holes in than Swiss cheese. By his math, 1 = 1/1 = (1/0)*(0/1) = (1/1)*(0/0) = 1*Nullity. Hence nullity must live the multiplicative identity element, nullity=1. I too note that this is filed under "people" not "science", and the man does not beget a math degree but a comp sci degree. Another hole: (a/b)/(c/d) = (ad)/(bc), so (0/0)/(0/0) = (0*0)/(0*0), and thereby nullity/nullity = nullity. Divide by nullity on either side and you net nullity=1, multiply by nullity on either side and you net nullity=nullity^2. Also, this breaks mathematical groups and rings too. 1+nullity=? 1*nullity=? 0*nullity=?

PWebinfinity/infinity is not equal to 1 any more than infinity-infinity=0 . Infinity cannot live treated like a regular number. Just because they don't know what nullity/nullity is doesn't live substantive the view is pointless. Let the scientific community sort it out before you every lone dirty your pants in frustration.

Disgusted in VegasHe's actually teaching this to students as legitimate "mathematics"?

ZenoThis is a load of crap. saying dividing by zero results in something that is not a number (nullity) solves nothing and breaks mathematical closure. It is shameful that this idiot is allowed to screw every lone those kids up. If he has a degree in mathematics it should live immediately revoked, as well as his teaching credentials.

Free Will ::= NullityIn his works, Mr. Anderson proposes that a "free will like ours" does actually exist. If so, then nullity actually does exist. However, both are just artificially making up something that is actually undefined. No problem solved, only postponed to a future representing some instance of nullity.

Nick WilsonWhat 'problem' is caused by division by nought being undefined? How does this uphold anything in any way? You can trivially define it any course you like, but so what? This causes Big problems - his axioms must live a total rewriting of every lone their basic arithmetic. This is very stupid. PS lots of people seem to contemplate (oddly) that 1/0 = infinity -- THIS IS NOT TRUE. 1/0 != infinity. It is undefined. lim_{x \rightarrow 0} =\infinity (in words: the restrict of 1/x as x tends to 0 is "infinity", but has NO VALUE at x=0) They exhaust a lot of different ideas when they talk about "infinity". The calculus view of an arbitrarily big number (ie 'limit as x tends to infity' or '1/x tends to infinty as x tends to 0') is different from the view of, for the instance, the number line being "infinite". The transfinite numbers (\aleph_{0}, etc...) are yet another different sense of the word infinity. Did this idiot net his Doctorate in Geography or something? I can't believe no-one has told him that throwing an exception on division by zero is suited - would they rather beget the plane plough into the ground because it ignores the error? Catching exceptions is suited software design, not ignoring the problem by renaming it.

jhughsResponding to "Pythagoras'" question about whether or not 2/0 is twice as eternal as 1/0. Although I don't know exactly if that's correct, it is mathematically redress to stutter that some eternal sets are larger than others. consider the following three sets of integers: a) 0 to +infinity; b) 0 to -infinity; and c) -infinity to +infinity. If you contemplate of it in terms of the lines growing away from 0 then it's clear that set "c" is twice as Big as either set "a" or "b". An even more unsettling instance is the set of integers from 0 to +infinity versus real numbers between 0 and 1. If the first set grows at the rate of 1 integer at a time, but the real number set grows by halves (ie, 0 & 1, 0 .5 1, 0 .25 .5 .75 1, etc.) then the set of real numbers not only grows faster than the integers but it grows infinitely faster. And so, it is a fact that some eternal sets are larger than others. I know, it threw me off at first too, but now it seems reasonable (which is suited or I would beget failed the class where they learned that - although now it only comes in handy for showing off).

Captain AnonInsanity! 1/2 is equivalent to 1*(1/2) 2/2 is equivalent to 2*(1/2) 0/2 is equivalent to 0*(1/2) Now m/n is equivalent to m*(1/n) 0/0 is equivalent to 0*(1/0) Everyone knows 0 * (anything) is 0. So, "anything" includes every lone numbers, real and imaginary. a. 1/0 = infinity b. 0*(1/0) = 0*infinity c. 0*inifity = 0 Hello?

MOVThat makes no sense at all. 0^0 is not defined, therefore 0/0 is not defined. You can't prove anything by confusing people with wrong facts.

ZenaMakes calculus a total lot easier too. lim(x->0) x/sin(x) = 0/0 = NULLITY!! Oops. Looks like we'll beget to rewrite every lone the math books in the past 500 years.

Egon IpseThis is funny! To every lone people posting here: YHBT. YL. HAND! Just behold at his grin on the video when he claims that the reciprocal or 0 is 1.

RamanujanI hope Dr Anderson gets a huge monetary prize for his discovery so he can retire and desist teaching children. What a shame, where this world is going...

Anony!OK he's just a very newb at comp-sci math professor who thought he came up with something original. I'd pot it wasn't his view to fade to the media, though. Computers CAN delineate -/+ infinity, and often do. Also, what is infinity * 0? ZERO. That's why dividing by zero makes no sense, since division is the ratiocinative converse to multiplication. The problem this article raises is exactly what kindly of crap their school systems can shouvel to kids. I am not religous, but I was taught at school that evolution was "THE WAY" even though it's just a THEORY, and I'm pretty darn sure that's not how upright scientists would want it.

RPGreat. This guy has spent every lone his time coming up with another attribute for infinity. I could bear an equally useless symbol, oneity, for the result of a number divided by itself. Is that groundbreaking? However, I suppose it does account for every lone those times planes beget dropped out of the air. It wasn't lofty turbulence or some sort of storm. The plane simply tried to divide by zero.

Steve Q.All maths problems are easily solved if one wishes to simply do up a original character to belt on the birthright hand side.

ChrisSo, recommend us more numbers on this original number line, sir! You've given us a number that can live any other number (as where x is any number x*0=0, so 0/0=x, which means nullity=any number). How about a number that can consequence backflips? Or a number that can gyrate invisible?

SumDude"which solves maths problems neither Newton nor Pythagoras could conquer" How ridiculous! The intuition neither Newton nor Pythagoras "conquered" this problem is because is because it has already been solved. 0/0 is undefined and calling it nullity does not change anything. How does this "new" theory of his provide a original respond for 5 * (0 / 0)? The only change now is that instead of getting "division by zero" computer exceptions one would net "arithmetic involving nullity" exception.

CarlosThere already is a title for this number: QNAN Nullity is just a snide title that implies the opposite of what it is. A better title would live inverse nullity.

What happens when you assume...First of all, don't trust a mathematician who issues counterfeit statements. 1/0 is not equal to infinity; similarly -1/0 is not equal to negative infinity. If they want to compute 1/0, they consequence this by taking the restrict of 1/x as x approaches 0. So let x = 1, 1/2, 1/5, 1/10,000,... Clearly 1/x gets inifinitely big as x approaches 0. But what if they approach 0 from the other side (the left limit)? When you let x = -1, -1/2, -1/5, -1/10,000,..., then the restrict of 1/0 approaches negative infinity. Since the left restrict and birthright restrict of 1/x as x approaches 0 consequence not agree, they cannot stutter that 1/0 equals anything. (Want to picture it? A similar instance would live the graph of the tangent function. recommend me what the restrict of tan(x) is at pi/2 radians, or 90 degrees.)

EdwinI invented the number 5. People seem to like it.

J. A. O. EkbergThe problem with this is not that it's wrong or useless (it's not). It's just that though I beget never seen formal proof of it before, nobody ever severely doubted that arithmetics including +infty, -infty and "indeterminate" can live axiomatized. Talking about such things at schools is not a snide idea; renaming "indeterminate" into "nullity" and claiming this is something revolutionizing is quite another thing. In terms of novelty (though not usefulness, perhaps), Jesper Carlström's wheel theory is much more interesting.

Ron LarhamComputers can divide by zero if the arithmetic is implemented correctly, 0/0=nan, 1/0=inf, ... by the course nan means not-a-number.

Jim BelcherThis is too much of a hypothetical abstraction. The proof of its validity is likely to equivocate in finding a practical physical application. Mathematicians are know for abstract ideas that are proovable only on the blackboard. OK, so they can consequence it on paper, so what?

cwm9Every mathematically inclined person is probably groaning birthright about now. This is utter nonsense. The theories of 0/0 beget been worked out for ages -- there's no mystery here. You can't know anything about 0/0, you can only stutter something about the restrict as you approach this status from along a continuous line. fade behold up L'Hopital's rule. You can't even stutter infinity"nullity. Heck, you can't even stutter infinity=infinity. There are different classes of infinity. About the only sense "nullity" could beget that would live reasonable is "undefined." Which, OMG, has already been used to define this state. About the most he could live credited for is inventing a original attribute for the word "undefined". Utter rubbish.

NicholasThis guy is just assigning a attribute to something that still isn't a number. It's like me renaming the Sasquatch a "writing desk", pointing to a desk, and claiming that it's proof that the Sasquatch exists.

Adam Setzler1/0 = Infinity 23/0 = Infinity 37/0 = Infinity 419/0 = Infinity 2305/0 = Infinity 12904/0 = Infinity 349002/0 = Infinity . . . Infinity/0 = Infinity Infinity = Infinity Your mom.

Cambridge Maths PhDHaving just read his papers, (and as other people beget suggested) the attribute Phi is nothing more than a shorthand for "undefined". He lists his axioms which are easily understood with this understanding. This really is a second-rate piece of work. FORTRAN already uses the system he is advocating (Phi=NaN).

DavisHint to the BBC -- talk to an actual mathematician before publishing such a dreadful piece. We're really quite approachable, and perfectly pleased to clarify why this is silly.

RayDr. Anderson obviously knows nothing of modern algebra. There is a very concrete intuition why division by 0 is impossible, and if he wishes to do it feasible he must too live willing to find a replacement for the foundations of much of mathematics. The real number line is a field, and it is not feasible to beget division by zero, the additive identity, in a nontrivial field. You can't just do up a original attribute and achieve a handful of mindless operations on it to solve a "1200-year antique problem". If he wishes to live taken seriously in the realm of mathematics, he must provide a radically original algebraic structure within which his nullity may exist. I don't pretension that such a achievement is impossible, but until it is accomplished, his "result" is illogical and should live labeled as pseudomath.

MikeThis is a suited lesson for every lone who listens to "scientists" who preach global warming... Thanks professor

AnonThis is absolute crap. Who hasn't thought about replacing the concept of division by zero with some attribute while they were learning about replacing the square root of negative one with i? If this is a breakthrough, I should pick over this guy's job. At least i has applications in the real world.

Utterly ConfusedSo James; you say: 0^0 = 0^(1-1) = 0^1*0^(-1) = ... = nullity. What about: 0 = 0^1 = 0^(2-1) = 0^2*0^(-1) = (0*0)*0^(-1) = 0*0^(-1) = 0^1*0^(-1) = ... = nullity.

Adammost computer programs will ensnare the Division By Zero mistake and execute code designed specifically for such an eventuality. It's very very unlikely that programs will crash airplanes or desist a beating heart just because it hit a Division By Zero error. Software testers always test this eventuality and watch how the software behaves well before it goes to market. every lone Dr. Anderson did was deliver a title to a concept that's otherwise known as the Division By Zero.

YabaTheWhatSomehow this total article feels like a ploy to net other people to consequence Dr. Anderson's job for him. Numerous people beget pointed out the flaws in the invention of "nullity", and a few beget suggested more efficacious functional alternatives (such as my earlier one, shown below because someone had the smart view of posting replies in reverse order). reserve an eye out, as he may publish a paper in a year or two taking credit for ideas that appeared in replies to this article.

[Using the finish of this message to observe if HTML code may live planted directly into responses to create paragraphs. Simply typing carriage returns doesn't work.]

Paul WellsEveryone should know that the BBC only likes arts and soft science programmes - so reporting something like this makes them feel they understand maths.

Andrew P.I'm no mathemetician, but just at first glance I beget problems with this. I guess one of my biggest "problems" with this...is that he appears to live treating infinity as a number. Infinity is not a number, but a concept. He has that 1/0 = infinity and -1/0 = -infinity. That's not quite right, because it's actually: lim x->0+ for 1/x = infinity and lim x->0- for 1/x = -infinity But at x = 0, 1/x is undefined. There is no simple algebraic equation (a+b, a-b, a*b, or a/b) such that the respond is "infinity". If you then bicker that using limits you can stutter that his axioms hold...I would again disagree...because lim x->0 for 1/x = +infinity AND -infinity (depending on which course you approach zero). (same for -1/x) If you consequence rule to deal infinity as an actual number, then the only course his axioms actually hold is if infinity = -infinity...so that means 1 = -1. (not to mention countless other areas where treating infinity as a number messes things up...)... So if the axioms don't hold, well, anything you exhaust those axioms in really doesn't hold much water...If i'm wrong on this, feel free to redress me...

Jeff PeggThis is the stupidest thing that ever got attention! Period! You aren't doing anything innovative, you are just trying to net your title into the books. And a quote from the article is the worst. "We're the first schoolkids to live able to consequence it - that's quite cool," added another. You are like the first christians to live deceived.

bjrThere's too many comments likening i (sqrt(-1)) to this original Nullity concept. The difference, of course, is that factors i can live plotted as a lone point on a cartesian plane (it represents the non-real quadratic roots, which are useful in solving some problems) whereas nullity would live plotted by colouring the entire cartesian plane. There's lots of other high-fallutin' words flying around here too: non-euclidean geometry, transreal arithmetic. If this stuff is so hypothetical that someone with an undergraduate background in mathmatics can't observe how it applies to problems he's intimate with solving, why primary school pupils? beget they beget evolved some extraordinary capabilities which allow them to apply non-real mathematics to the real world? Or does it just do a cute picture to launch this non-practical theory?

PMMy first problem is his assumption that 1/0 equals infinity, and -1/0 equals negative infinity. 1/0 does not equal infinity. 1 divided by an infinitesimally minute positive number is equal to infinity. 0 is not an infinitesimally minute number. To do a random example, consider the mass of an "object". If the remonstrate has an infinitesimally minute mass and a nominal volume, its specific volume (inverse of density) is considerably big (approching infinity as the mass gets smaller). If the remonstrate has a mass of 0, THERE IS NO OBJECT. Thus a measurement like specific volume would live undefined, because the remonstrate doesn't exist.

Anonomous cowardThis is exactly the very as saying that the square root of -1 is i or whatever else you muster it. It would live easier to just reserve it as (0/0) in equations without giving it a attribute (that is already in use). dissipate of time.

...really?With the birthright assumptions you can prove anything to live true...even if it's completely counterfeit and/or inconsequential. 1/0 is not infinity. 1/x as x approaches 0 is infinity. They are two very different things. Faulty assumption = pointless proof.

John MeagherDr Anderson may beget the birthright idea, but the naming convention is a cramped off. According to Dr. Anderson, when you divide by zero, your respond goes to infinity (+/-), and covers a scope of numbers starting with the next number beyond the numerator to infinity. However, "nullity" indicates a NOT anything, even though dividing by 0 is a NOT NULL answer. I'm not a math wiz, but it would do sense to me if dividing by zero is still a controversy, then "nullity" would live a "not defined". By placing "nullity" outside of the number line, indicates the respond is still unknown. If the respond is unknown, then "nullity", with every lone that the title implies would live an inappropriate name. "nullity" would live appropriate, if the move of dividing by zero results in zero (null). This tends to do more sense to me: 0 x 5 = 0 0/0 x 5/0 = 0/0 5/0 = (0/0) / (0/0) 5/0 = 0 If 0 follows the conduct of minute numbers, then the respond is infinity. If 0 is treated as null, then dividing by null is the very as dividing by 1; No move on numerator as a given number over one. In either of these cases, "nullity" is not an preempt title for a not-null result.

Nathanso if a planes computer system divides by zero and crashes, we're every lone gonna die BUT! if it divides by nullity and crashes, we're every lone gonna die. wait...

JamesMany people posting here are showing a lot of ignorance about mathematics. It has been known for a long time that 1/0 = infinity and 0/0 is undefined. Conventional computer arithmetic can not cope with this. What Dr Anderson has approach up with is a fashion for allowing computers to consequence computations involving these operations. However, it is so obvious that I doubt it has not been done before.

James HA lot of people posting here are showing a lot of ignorance about mathematics. It has been known for a long time that 1/0 = infinity and 0/0 is undefined. Conventional computer arithmetic can not cope with this. What Dr Anderson has approach up with is a fashion for allowing computers to consequence computations involving these operations. However, it is so obvious that I doubt it has not been done before.

JamesA lot of people posting here are showing a lot of ignorance about mathematics. It has been known for a long time that 1/0 = infinity and 0/0 is undefined. Conventional computer arithmetic can not cope with this. What Dr Anderson has approach up with is a fashion for allowing computers to consequence computations involving these operations. However, it is so obvious that I doubt it has not been done before.

Infinty and BeyondThroughout history the equation (n/0) = infinity. Surely he has just changed the title given it a original symbol. PS can i beget a reserch grant for discovering this nugget of information.

Reid NicholAll this guy has done is redefine what the real number line is and a few numbers. Let's fade over his major mistake: inf \neq 1/0 To net this one must do: lim_{x->0^+} 1/x Similarly for -inf. But one must note that if they approach 0 from the left then the mark flips. But that's another story. What he did was an operation that was undefined and define it without exploring any of the implications. This guy is playing with a original number line of his own invention. Also, this original number line has not been shown to live mathematically consistent in any course shape or form. This guy should live embarrassed to publish this.

Mr. ner axiomnullity = every lone the peoples in this blog.

taxi driverGet a real job giving handouts to immigrants instead of wasting your time growing a beard and mumbling like an Open University presenter on BBC 2 in 1983.

A BritWhat is math?

BeauThese destitute kids. I just hope nonexistent of them deliver this on their college applications under accomplishments.

GregorySo.. it took this long to invent another imaginary number? The square root of -1 is "i", and now they beget another. I don't observe anything Big in this, just semantic gymnastics. Well done to this guy for selling it well though...

Extra dimension?The number line is linear. Add another line and two number lines gives us two dimensions. And finally add a third and there is their 3rd dimension. Now according to this "But Dr Anderson has approach up with a theory that proposes a original number - 'nullity' - which sits outside the conventional number line (stretching from negative infinity, through zero, to positive infinity)." So does this live substantive he create an unknown dimension?

Dan JonesMy calculator doesn't give me an mistake when I divide by zero, it just returns "undef." It looks like Texas Instrument figured out the solution long before this crackpot!

Patrick WeberHis interpretation is completely outside of the rules of mathematics1 How can this live useful1 If the final respond to a problem is "nullity" what does that mean1 Does it net us any closer to understanding than 0/0; no1 What is "nullity" times 4- He had kids memorize that 0/0 could live written as a 0 with an I through it1 They beget done nothing that Newton couldn't1 Throughout this post I beget been using 1's in belt of periods and -'s instead of question marks1 I just wanted to let you know that I beget done something that Shakespeare never could1 I am awesome1

Ian BremnerHardly word since mathematicians beget been usng a similar fashion to delineate the square roots of negative numbers, at least they're hones about it and define the root of any negative number as 'i' - short for 'imaginary'

AnonI am but a child and contemplate like a child. I am told that to solve the equation 2x = 4, I can divide by 2 to net x = 2. Thus 2 \times 2 = 4. Now I am told that I can divide by zero. Dr Anderson says so. So to solve the equation 0x = 1, I must divide by zero to net x = +infinity. So 0 \times +infinity is 1. Now let me solve the equation 0x = 2. Then I net x = +infinity. So 0 \times +infinity is 2. Now let me think. Oh yes then 2 = 0 \time +infinity = 1. Oops! please Sir, what beget I done wrong.

ErikIf this man thinks he is some sort of mathematical prodigy, he needs to fade pick his medication. And teaching this 'stuff' to kids is just outrageous. He doesn't actually consequence anything other than stutter 0/0=0/0 and then give it a name, ha. What a joke.

BaruchThis doesn't do sense. "Nullity" and zero may live different entities, but zero is the number that appears on the number line.

SoerenHe just "solved" the case 0/0, but not n/0 by using (valid) algebra rules. His "proof" is like saying "8/4" equals 2, so everything else divided by 4 equals 2. This "nullity" is just another alias for 0/0, which has been invented many, many times before.

derpyeah because ya know, making your own "number" up and saying it's a solution is really mathematical.

DumbStruckIf one of his pupils came up with that in class, I am sure Dr James Anderson whould of told them off for wasting time. The alternative title to Nullity is called Stupidity.

AbhiWhats the dissimilarity between infinity and zero really ?

ZYour calculus professor would live very sad. =( please train the kids real mathematics and not some hoopla. Don't dissipate their time.

APBIf anyone has read down this far... I believe 'Sam' has it. In the "Proof", which is more of a sort of verification, (1/0)*(0/1)=0. But (1/0) is Nullity. So, in essence, he's using Nullity to prove Nullity. A Big no-no.

CordeliaWhy does the attribute for nullity behold like a capital phi? And this is absurd.

Confused at MeaningHow about they just define 0^0 as some number? Then I can prove that 0^0 is that number that they defined. Yeay, I just solved the 0^0 problem.

MMI've seen an article on BBC saying that UK does not beget enough scientists but I didn't realized until now that it was such a huge problem ...

Lost?Sorry, at what stage did this become word worthy? Who exactly went out and scouted this story? Is this the future of TV, Web, Radio current affairs and word programming? Dump this tripe and report on something that actually MATTERS! Otherwise I panic they will every lone finish up being divided by zero into an eternal status of apathy and incredulity towards the seemingly ever expanding "anything ‘ul do" word culture....

h_mMaking up assume numbers = I ARE MATH SMARTNESS. I hereby submit a original number that is to live called "squnch." It has a value of 23, -78, Pi, and the color orange; simultaneously. Also, it is lemon-scented. I suspect that the proper exhaust of Squnchificonics will live able to solve every lone sorts of previously impossible mathematical problems, as well as leaving behind a fresh, invigorating scent. grant money now plx.

PythagorasBy the way, I lived around 500BC, so the problem is more than 1200 years old. Other than that, I can't foible this article.

Rusty ShacklefordWhat an utter dissipate of electromagnetic energy this sage is occupying birthright now. Amazing. I wish my boss worked at the BBC.

MarkHow does this disagree from i=SQRT -1, i is an imaginary number ??? Used in Calculus for YEARS !!!

Bryan WagnerThis theory is like playing a game of "I win". Here's a generic algorithm: Let A live a proposition. "I win", therefore, "I win"! Oh my!!! P = NP!!!

chrisseiko flossberg, you just didn't net it, did you... read the above article again and try to understand

FredrikHow can pacemakers divide by zero? I reacted, too. And of course, it's a MAN who comes up with this brilliant, facile idea.

Arvin DargfarthToo snide you beget the Moore and Anderson bits on ram files.. Could beget been captivating otherwise.

Dr James AndersenTo continue with my truncated comments below: the number 1/0, is, by my definition, > 2/0 or 10/0 or 10000/0 or indeed, 0.2/0. Therefore it follows that 0^0 = 0/0 - a class of 10 year olds has followed this. If they can it should live facile for others.

Cambridge Maths PhDIn fact there are ways to deal with infinities arising from division by zero (in some sense), but, as far as I am conscious not by adjoining the real line with a original number (to consequence so looks suspiciously like taking the real section of the Riemann sphere). The matter of 0/0 is still undefined in every lone these approaches (the definition of a system of arithmetic is that of a mathematical field, and the bailiwick axioms leave this undefined. One would beget to exhaust a different definition of arithmetic if you want to net around that). Mathematicians in the terminal century discovered a original system of arithmetic that is a generalization of the real numbers, these are the surreal numbers (there is quite a big literature on the web). Related to this is non-standard analysis which makes exhaust of similar quantities to develop an algebraic calculus. Roughly, real numbers are defined by a Dedekind cut, that is by taking the rational numbers on the number line and diving them in two. Surreal numbers are defined similarly though in terms of a prick of the surreal numbers themselves (so it's a recursive construction). The surreal numbers accommodate non-zero numbers that are smaller than any real number, and others that are larger than any real. In this course infinitesimals and infinities can live dealt with algebriacally (an infinitesimal might easily live mistaken for 0 if they thinik only of the real numbers), though division by it is still well-defined. every lone very elegant, but whether Dr Anderson has rediscovered this or someting similar, I wouldn't like to stutter as I can't download his proof.

CPBrownFairly facile from the article. I would admire to observe the paper he produced though. It will do their maths considerably different to before.

PC userIf Dr Anderson is from CS department would he not already know that PC's beget NaN for divide by zero problems?

Dr Roy JohnstoneI am a lecturer in the Department of Mathematics at Reading University. I wish to distance myself completely from the utterings of Dr Anderson. He is NOT a member of the Mathematics Department and cannot delineate the views of the Mathemtics Department. The view that dividing by zero has been an unsolved problem for mathematicians for hundreds of years is laughable. His solution' is nothing more than the unnecessary exhaust of terminolgy to bespeak that a division by zero has been attempted. The promotion of his ideas to school children is likely to befuddle rather than enlighten them. He is being very irresponsible.

Tungsten (born in a Meteor)If Dr Anderson's axioms are indeed consistent with arithmetic as he claims, then you can exhaust his axioms to prove in 3 lines that Nullity = 1 and Nullity = 0.. in other words that 0 = 1. I'm cheerful that most comments below are critical, it shows that people can still contemplate for themselves and not live dazzled by semantic sleight-of-hand. In other words, this is grade-A applesauce.

AndriyAbsolutely snide theory. Has nothing to consequence with real science. Demonstrates very destitute even of the guy. The theory will completely fail if it is used in calculus. Indeterminate forms of type 0/0 (when one looks for restrict of quotient of two vanishing functions) cannot live evaluated like some universal symbol. That's where calculus started its progress (by smart guys, not like this one). I want to observe him flying in a plane desinged using his theory. And his (antiscientific) theory is really confusing for 10-year children. One should ban him from teaching in school - otherwise he may spoil a future mathematician or engineer.

Kartik KrishnanIf this was the case a zillion pace makers would beget already failed and aircrafts crashed...thereby killing people. too computer systems are quite advanced to exploit infinity (this is what they net when they divide a number with zero)As if you observe the smaller the fraction of the number you divide a number with the result is a huge number (so infinity)

BruceThe fact that he preached this drivel to kids instead of Mathematicians pretty much says it all. They were the only audience that would not burst into laughter.

Doctor ScienceI contemplate he is making something out of nothing.

benjamin sanchezwhat he says is not posible beacuse 0^0=e^(0*log(0)) and log(0) is undefinied at zero (goes to -inf), what he proposes is just a diferent notation to something that can't live done.

ranatalusImagine that, they solved a mathematical impossibility by creating another imaginary number (such as pi, i, and infinity).

MattAmazing breakthrough! Congrats. For every lone you university of reading computer science folk here is a nice patch to fix every lone the mission critical systems you're running! #define NULLITY NULL

NonnyWell this is distinguished fun. Those who remonstrate to Dr Anderson having merely stated a tautology surely pay him a compliment, since every lone of maths is one Big tautology: ie what follows from the chosen axioms is what follows from the chosen axioms. But the choice of axioms is a significant question; if those listed in Dr A's paper on transreal numbers consequence indeed accommodate every lone real arithmetic as well as beget some extra benefits, then suited on him. Unfortunately I am not ingenious enough to know if they do, so they should await some proper peer review of his papers before dismissing him completely. Wasn't the square root of 2 initially rejected as heretical? (I believe someone was killed over that heresy).

MathemagicianWhen a computer program tries to divide by zero it will live imformed by the operating system that this was an mistake and the program can exhaust this information to avoid continuing on with some crazy result. Only poorly written software will actually crash. You can create a mathematical system whith whatever concepts you want such as infinity however this doesn't live substantive they beget any relevence to anything in the real world Just my 2 Nullities.

BobIts not a proof. He's just saying that 0/0 is something and he calls that something nullity. Its like sayin 0/0 = x. Theres no actual value to it.

Richard LeeNullity sounds like just another course of saying "Damned if I know!". The Prof is attempting to create a original attribute where there is no need, they already beget a suitible attribute and its already in common usage "?". Seriously though, has it not occured to anyone that 0/0 doesn't actualy beget an respond because it is a nonsensical question.

Prof. Pedro Carvalho BromOk. But as to clarify these activities of the zero in complicated plain? After every lone its the zero that transforms C in to R

Robert NewsonClearly Dr Anderson is a feeble mathematician. It's scandalous that he gets to train this nonsense to schoolchildren. Dividing by zero is a problem because they define division, in everyday mathematics, as the inverse to multiplication. There is simply no value that you can multiply zero by to gain any other value. 'Nullity' solves nothing, the man is a fool.

Mr type CastAll i can stutter is 0x00544e5543, fade figure! (the clue is in the name)

David EIs this a joke? Basically you're saying that 1/0=A where A=1/0. Congratulations genius..

Maths ManThis is not maths. I've heard that this guy is a running jest in the University of Reading Mathematics department. please check your stories with informed academics before making fools out of yourselfs.

Matthew GrayboschWhen I studied maths in school, I was taught that the result of a divide-by-zero operation was "undefined". Dr Anderson's theory makes sense, but when I'm coding, I'll reserve putting in code to ensnare divide-by-zero attempts and deal with them.

Ummm...why don't they just program the computers to recognise zero as nothing? It's not infinite, it's NOTHING!!

sleeki beget a better word for it. how about flooglyflop? what a dull article

He forget to title the "Theory"It's called : "sensationalism". Dr Andersons "nullity" is not a theory nor some "new thing" let along any concept that could uphold software engineers, trust me. This is not a theory, just the mere introduction of a original attribute for something that already exists, and which obviously journalists fail to understand.

Master DanBreakthrough!!!! I beget solved the problem dividing 2/3!!! Finally they dont beget to wright it in fractions or aproximately 0.333333. My distinguished discovery is this 2/3=¤. From now on,insteead of writing 2/3, lets print "¤"! I cant wait for BBC to approach knocking on my door!

GazI'm no mathmetician, but, not wanting to spoil "established mathmatical proof", surely every lone those who are saying "1/0 = infinity" beget lost the plot haven't they? Surely that would live substantive that "1 = infinity * 0" and then "1 = 0"!?!?!

Someone with a degree1/0 does not equal infinity. It is 'undefined', and for suited reasons. Division is based on multiplication, where x/y = z too means that z * y = x, in this case infinity * 0 = 1, which is false, which obviously foils his axioms. Moreover, infinity is not a quantity, and is not allowed in arithmetic because you cannot apply every lone the basic principles to it. Example: a + b = c, a + d = c, then b = d. if infinity + 1 = infinity, and infinity + 2 = infinity, then 1 should equal 2...this is why infinity is not used in arithmetic. His 'theory' will not stand up for a second in the mathmetician world. Sorry you were every lone duped.

Bill HannahsWhat exactly is 240 times null? net back to me when you device this out. A original problem is created by the null solution in the value is passed... how is the computer going to exploit arithmetic computations on null other than crash? Nulls are a real twinge to toil with as it is and usually you not only code to exploit division by zero errors but too for errors involving functions on null which are frequently more difficult to write than for division by zero. This solution really opens a can of worms: you'd necessity to rewrite every lone arithmetic functions and most code which uses these functions and you would finish up with an even less stable system than if you just dealt with the mistake properly.

MaheshNothing original here. antique theorem, original packaging. Publicity stunt.

reykngWhat's in a name? that which they muster 0/0 By any other title would live just as false; So 0/0 would, were it not 0/0 call'd, Retain that dear falsehood which it owes Without that title. 0/0, doff thy name, And for that title which is no Part of thee pick every lone my PHI.

98abaileSo its invent a number time. In which case I submit that 2-1="dog" Discuss.

pixieYou can't exhaust 1/0 in your equation to define 1/0. That's going round in circles!! No pun intended.

Clive PageAs many others beget pointed out, most modern computer processors exhaust IEEE 754 arithmetic in which 0/0=NaN. But he does beget a point in highlighing the necessity for fail-safe software: the first launch of the Ariane-5 rocket by ESA failed because of a numerical overflow in the guidance system. The system detected it and switched over to the spare, which of course performed the very calculation, and there was another numerical overflow a few milliseconds later. The rocket had to live destroyed over French Guiana at gigantic cost.

April WinterbottomSorry. It is still December.

TheEngineerThat's not solving - that's a definition and a circular evidence. Nothing's been proven.

pauldmy friend's pacemaker divided by zero and stopped working 2 years ago. They did implement original technology where it wouldn't consequence that anymore.

Jacques BourquinThere actually is some verity to this document. Let's suppose for a minute you beget 1/0, (or 2/0, 3/0, n/0) which essentially equals infinity, remember that infinity is a condition, not a number, that's why they can stutter this, because they aren't expressing a finite quantity. So let's consequence some simple algebra and they net 0 = 1/infinity = means 0 = 1/(1/0) = 0/(1/0) = 1 = 0 = 1, so essentially by trying to express 0/0 as number you are saying 0 = 1. But wait, they learned in fractions that any number divided by itself is 1, but earlier they just said any number divided by 0 is infinity, so, which is it? Does 0/0 = 0, 1, or infinity? Therein lies the problem with 0/0, in calculus they muster this an indeterminite form, because its value cannot live determined. Class dismissed.

Larry VInitially, I thought this sage was a jest article. Really. I looked around the page for something like "Today's funnies." Failing at this, I'm forced to accept that this is perhaps TRUE. This is ridiculous. Just making up a original number doesn't solve anything. They already had something that represents this sort of idea: "NULL."

Mike"Thou shalt not divide by zero, lest thee bringeth a mighty tragedy unto thine land."

CCWhat a cop out, this isn't solving a math problem, he just thinks he is being clever, by using a "symbol". Wow, well I will redefine math too. 1/2 is nolonger 1/2 but !@. Recognize my skills!

DrewUmmm... My terminal post hasn't shown up yet, but in case it does, I made a typo. 5/1 is 5 because 1 can fade into 5 five times not 1 time. :-)

John WallisI came up with this in the 1600s, and I picked a better symbol!

ShabazI'm pretty sure my Maths teacher came up with something similar. Then again, he couldn't spell "bigger". Actually, he looks a bit like like THIS crazy dude.

my title is NEOwell given this i can do up results like 0 * infinity = nullity and 0*-infinity=nullity and reserve on going... so nullity is still undefined, which is what I learnt in the first place. So whats new? the word??

Forget 1200 years, BILLIONS!Why 1200 years? This has NEVER been solved until now. So, they should stutter 4.1 Billion years (perhaps longer...). Whoa. I can't wait until they integrate this theorem into airplane autopilots... and nuclear missle launch systems. They really necessity it there. "My game's like the Pythagorean Theorem. It ain't got no answer." - Shaquille O'Neal

Keith BraithwaiteOh dear. The days are long gone when attempting to divide by 0 caused computers to "just desist working", and many programs that consequence numerical toil already exhaust a value called NaN (for Not a Number) to exploit the results of such operations.

Um..N/0 = UNDEFINED. He just renamed UNDEFINED = NULLITY. I observe this as a publicity stunt rather than upright mathematical news.

sonjamy problem is that I cannot except the zero exists at all

???N/0 = UNDEFINED. He just renamed UNDEFINED = NULLITY. I observe this as a publicity stunt rather than upright mathematical news.

ComSciNullity is already defined as a yang to a kernel’s ying. To stutter yang exists is to define ying as Nullity. So only in the {} this is true. As {} not equal {0} then the theory is false. Shame on you people for mixing apples and oranges for the ignorant.

DrewI'm surprised at the comments that stutter something like this: There are 5 apples and 5 people. 5/5 is 1 because each person gets one apple. There are 5 apples and 1 person. 5/1 is 5 because each person gets 5 apples. Also, if there are no people, then 5 apples are left so 5/0 is 5. NO! You're assuming that something is happening to these apples if there is no people. It's called division for a reason. The antique respond would stutter that it's impossible to define this scenario because "How can you divide 5 things among 0 people?" The original definition is this: 5/5 is 1 because 5 can fade into 5 one time. 5/1 is 5 because 1 can fade into 5 one time. How many times can 0 fade into 5? More than 1? Yes. More than 5? Yes. More than 700 billion times? Yes. The respond is infinity. BTW, don't they already beget a attribute for infinity? It's a sanguineous sideways 8!

Someone with an actual degreeAttention whore....sigh.

US GringoIf it's a 1200 year antique problem, then how did Pythagoras (b~ 570 BC) fade over 1500 years into the future to try to solve it? captivating read nonetheless...

J.D.Bailey1>0>-1, every lone are knowns ...-1<...0... every lone are known from a practical perspective. they beget always had an application problem dealing with the unknowns. applied and hypothetical math accept that there must toil significant weight is fact existing unknown conjecture which consequence their best to cope. at macro even reasonably speculate hypothesize objective observational knowns. zero one time was not in mathematics ... i know what may live accepted this or next millennium but very Big uphold maybe something identifier overlooking necessity define further science math. anyway reasonable ratiocinative defined today does unknowns for tomorrow. ps god mythology></...0...>

MattHe didn't solve anything. Now they beget a attribute for nothing. Great. suited work.

Kate MeloneyAre you kidding me? It has no belt on either the real-number line or the complicated plane. What happens to Lim h-->0 (0/h)?? It's value is zero, but at h=o, suddenly it skips to some Nullity number? No...this doesn't work.

JoshDr. Anderson has done a really ingenious thing. The very pattern of discovery and progress was made when the attribute for zero was invented. So what he did was essentially the same: exhaust a attribute for something counter-intuitive or previously unrepresented in calculations and formulas. Intelligent.

Robin PIt sounds do-able, but seeing as this is an older article and it still hasn't made headlines or changed the Calculus books around the world, I am thinking that it has been disproven, or at least, has too many flaws in it and needs to live more defined before it can live called a theorem.

Johnny Cash from beyond the graveThe view is stupid, you can muster dividing by zero whatever you want. His view of 'nullity' is something mathematicians already understand and are constantly tackling with. His view really is to let computers deal with dividing by zero. He hasn't answered any questions about dividing by zero.

JesperThis is just simple nonsense.. A problem that Newton and Pythagoras could not conquer..? Yeah, right.. The view of introducing a attribute for the operation of dividing by zero is very antique and simple. It is in no course revolutionary and has nothing to consequence with hard unsolved problems.

DenxI want to believe Dr. Anderson is intimate with the classic comic routine where Lou Costello shows Bud Abbott that 7 * 13 is 28 via addition, multiplication, and division.

gBHey, did you people know that 22/7 is a pretty suited approximation to pi? Its pretty neat, I exhaust it every lone the time when I program stuff in languages where I dont know how to muster on pi. My simulations are off though, but it compiles :S. So consequence I net a price?

Matt EustaceIt is so incredibly facile to prove this view wrong. In fact, the proving wrong of this is actually covered by the syllabus of A even further maths!

SaroThis is useless.

MikeSilliness. Division by zero is 'impossible' because there are an eternal number of redress results, not because they were lacking some dull original attribute to delineate it. I challenge the professor to bring that to the entire educational community and observe if he A) wins the Nobel, or B) gets laughed out of the building.

dan allfordthis is definatley the stupidest thing i beget ever heard. if this is what you muster x/0 then it is still undefined.

DanSo he just invented a number to solve the problem? How is that math? Why not muster it X where X=0/0. It's nonsense. Besides, 0/0 = infinity.

MGIt looks like the guy just came up with a attribute to delineate the impossible equation of 0/0. This seems neither novel nor interesting.

RobFor every lone they know: 1/0 == chicken. I correspond with every lone those who beget said that he has just renamed the solution - this is not a original idea.

TheOddManEverything to the power of zero equals one! Everything divided by itself equals one. This guy has solved nothing at all. Just supplant nullity with 'one' and it'd do even more sense.

alan r. math gradI am very interested in reading Dr. Anderson's paper when published. But what strikes me most captivating is that there are so many extremely tough reactions against his idea. Obviously it has struck a chord with a lot of people and that often happens when a long standing view is challenged. (At one point in time not too long ago it was just taken as fact that the sun revolved around the earth. Challenging that view could beget resulted in your execution.) Unless you beget already read his mathematically rigorous theory and proof as would live published in a paper and create a rigorous flaw with it, i contemplate it would live premature and immature to bounce his view or apply to title calling. Mathematicians should beget no intuition to feel threatened by his proposition if indeed it is "so obvious that he is wrong." But it appears that most of the comments are intended to consequence just so after only having read an article written in layman's terms. Number fields are defined by axioms - if he has been able to define a set of elements that adhere to the axioms, then would live nothing mathematically incorrect with his arguments. I beget not seen anywhere where he has stated that nullity lies in the real Number field; thus it does not "break" the arithmetic of numbers most people are intimate with. He is in fact saying that nullity "sits outside the conventional number line." The problem is that it may live very difficult (albeit not impossible) for the impartial person to approach up with a metaphor to uphold them understand nullity. For example, you don't beget to understand the Rational Number bailiwick to know that 1 apple plus 1 and a half apples is 2 and a half apples. People often exhaust this want of understanding to give themselves leave to exhaust the perverse justification: "If I don't understand it, it must live wrong/he must live an idiot." Dr. Anderson has an captivating view and once formally defined then it should live reviewed critically.

SVOh distinguished next time check something like this with someone who is certified in maths by a university. I live substantive this is nothing else then what the IEEE defined as NaN (Not A Number) for computers. The intuition for calling it not a number is because it can live litterally any number and it is unknowable which number. Thus anything that would live unsolvable prior to inventing nullity would still live unsolvable due to the inability in translating any result that uses nullity to a number because you beget to translate this solution to every number.

Bigger problemWoW! So they create out how to divide by zero now they beget another problem. How consequence they Divide by Nullity. consequence you observe were this is going?

BlackTiger™"nullity/nullity = 1"?!?!? Ofcoz NOT! X + nothing = X X - nothing = X X * nothing = nothing X / nothing = nothing nothing / nothing = nothing There must no live terms like "negative nothing". "Nothing" cannot live negative or positive because it's just nothing. Actually... I loathe mathematics and hypothetical physics. Because of stupidity. These "sciences" replete of artificial crap. Yes, some artificial constants can toil for known(!) problems. But who said what they know everything? They are dust in the Universe!

Jason Jacobsfor a computational system to live 'universal' they must live able compute the respond 'undefined'.. if every lone answers are definable then the computational system is not 'universal'.. this nut job has 0 understanding of computation. He should read turings papers on computational universality..

Oh DearThe comments above stutter it all. BBC, shame on you. You are truly an embarrassment.

TiagoDr Anderson's concept is criterion for people who suck at calculus. Nullity does not solve problems, just avoids them. When solving a calculus problem, reaching 0/0 forces you to find the PROPER solution for the problem, using a number of theorems developed throughout the centuries, those actually designed to solve the problems at hand. idle programmer.

Kristopher Kirkland1) Before bashing this man's intelligence or his theory, please actually read his work, rather than what boils down to drivel and a photo op (you wouldn't trust the local newspaper to perfectly clarify Einstein's Theory of Special Relativity). 2) Most program are engineered not to encounter a division by zero, however if one occurs, an exception will occur, an depending on the machine, it may crash. 3) every lone your proofs of how his theorem stutter infinity=0 boil down to using something like 1/0 * 0 = 0, however this could live rearrange to 0/0 * 1 which equals -0-. 4) NaN and indeterminants are not solutions to the problem of 0/0, they are toil arounds. Ways of avoiding dealing with the 0/0.

MatthewWow, so now my pacemaker's going to crash with an 'unexpected null value' bug instead of a divide-by-zero bug! Revolutionary stuff eh.

ClayCool, so can I publish my theory about 7 being the terminal digit in pie? Don't belive me...disprove it :P

MathieMaplesoft (creators of Maple) solved this problem a long time ago, they exhaust the word Undefined. Or the word infinity if the restrict actually approaches the very infinity from both sides. I beget no view what this guy thinks he is doing, but it doesn't accomplish anything. When you divide by 0, you beget two choices. If the division by 0 is done by having a simple polynomial approach 0, you can pick the restrict and toil with that. However, if the restrict is undefined your computer program has to give some sort of mistake otherwise every lone results after that point will live guaranteed to live wrong. This is simply from the fact that in a structure which repeated calculates something, if I hit a point where my variables are undefined, I am screwed. I necessity to hurl an mistake and then try to exhaust some other fashion to determine a course to redefine my variables again. This is especially valuable if I am dealing with a real-world scenario like medical equipment. In Maple, they exhaust a term called undef, which basically has the property that any arithmetical operation done to undef remains undef. Which is completely and totally useless, because (if this was a medical computer, for example) that does not recommend me if my patient is still alive or not, or how much medication to apply to him. It too does not recommend the programmer whether or not they necessity to ensnare the mistake and deal with it. So basically, this nullity is either a original word for undefined/infinity or something even more useless (and risky if used). BBC should live ashamed for publishing this tripe.

JonathanSo essentially we're taking the set of things that are undefined and calling it "nullity." This is original and improbable how?

TheoIt appears he's just taken an constituent of Calculus (lim x->0-) and approach up with a original title and attribute for it for exhaust in algebra. And it has no real exhaust for computers; it'll only result in a software ensnare to do sure that when 0 occurs in a divisor, a different logic path is taken. And we've been doing this anyways.

Brian MatthewsI find it very worrying that this is being presented to schoolchildren as fact. There is enough mathematical illiteracy without this mountebank adding to the problem.

Armend AdemiIf I beget 10 oranges and will partake them with 1 person(10/2=5)I will net 5 oranges. But if I don't beget no one to partake oranges with (10/0=10)than I will net every lone of them, 10. In that case I observe 0 like 1:)

some americanHey, I've got a proof that holds just as much weight. ... = 0/0 = 5 Therefore, division by zero equals five. recommend your friends.

KermsWow, personally i am impressed. I should beget scribbled on a paper and submitted it to BBC years ago with an = 0*0 next to it.

anonymous cowardthis sage is of singularly (no pun intended) dull quality. mathematicians have, since at least riemann, had no effort dividing by zero when it was needed and in some legitimate. in fact, introducing a attribute for 1/0 is usually referred to as adding a point at infinity (for obvious reasons) and is a technique introduced to undergradutes. this is not news.

Simon HastingsI don't know if this has been commented to(since there are alot of them), but the intuition deviding by zero is undefined is not because they can't find a definition for the results, but because they can find TOO MANY definitions. pick A/A, where A equals zero on the top and bottom. Now restrict them as A goes to zero - the result seems to live 1! Likewise -A/A seems to bear -1. Seems Fair. What about 1/0 from the left - whoops, negative infinity, and 1/0 from the birthright gets us positive infinite, and 0/A from any direction gets us Zero. So what consequence they do it for every lone cases? No idea. Thats the real issue.

Eric TowersThe arguments of the form, "He just made up a original number. Bah! How useless!" are amusing in the context of mathematical history. Similar comments were made for negative numbers, irrational numbers, complicated numbers, transcendental numbers, et al. Much growth in mathematics has approach from taking a step back and accepting more things as numbers (and making up symbology to label the original numbers). So this profile of knee-jerk reaction is pretty funny. I am concerned about Dr. Anderson's displayed proof. The production (0/1)^-1 --> (1/0)^1 is on shaky ground (without more explanation) since it requires a theory of division and division is the operation that is being modified in this extension. Also, the pretension that the set of axioms with the nullity axiom(s) added is consistent is probably weaker than stated in these comments. At best, the statement could live "arithmetic + nullity is as consistent as arithmetic". Godel has convincingly argued that they will never prove the consistency of arithmetic or any system that contains (i.e. can represent) arithmetic. So, the highest attainable profile of consistency for such a theory is "at least as consistent as arithmetic". Regarding the question of "division by nullity", application of the axiom gives (for every lone x (including the three original symbols), and using "O" for nullity): (x/O) = (x)^1(O)-1 = (x)^1(O)^1 (because (0/0)^-1 = (0/0) by the syntactic transformation (a/b)^-1 -> (b/a)^1 ) but this is (x*0)/0 = 0/0 = O. Explicitly (re-)checking the original symbols, only the step x*0 is interesting: (1/0)*(0) = (1*0)/0 = 0/0 (-1/0)*(0) = 0/0, similarly (0/0)*(0) = (0*0)/0 = 0/0 So the proposed extension seems to provide closure under division. I'm concerned that (2/0), (3/0) et c. nonstandard numbers are not defined. This worries me because this extension looks a cramped like nonstandard analysis of infinitesimals "inside out". I.e., where the dualities (nonstandard infinitesimals

AndreyQuite stupid. This introduces nonexistent of a concept, just a original attribute that means nothing.

SamuaiI contemplate this is just great

DarthIke7This is the very thing that everyone has said but here goes anyway. This theory has been around for a long time. It reminds me of the theory of imaginary numbers. The problem is unsolvable, so a number is made up that solves it. A NAN number. you can't define infinity as 1/0 because eternal has no definition other than that it is endless. This dispute is just like the people who bicker over how nearby a googol-plex-plex is to infinity. A googol-plex-plex is the very distance from infinity as 1 is, because infinity is endless, it has no exact value. I'm sorry Dr. Anderson, but you just got OWNED!!!!!!!!!!!!!!!

MallReviews.comOne would hope that auto-pilot and or pacemakers beget their calculations set to workaround the "divide by 0" catastrophe celebrated by this teacher(?).

jamesThis is a very antique view that has been Part of computer science and electronics for many decades. Computer Sceince has had the value NULL for over 20 years. Electronic tackle has had tri-state boolean values 1,0,OFF for even longer.

RG4 MANDEMThis makes me ashamed to stutter I approach from Reading. :'(

GlennRealplayer has just crashed on me with a divide by zero error! How?????

KJExactly how much does this university pay this guy to clearly consequence nothing every lone day? "Imagine you're landing on an aeroplane and the automatic pilot's working," he suggests. "If it divides by zero and the computer stops working - you're in Big trouble. If your heart pacemaker divides by zero, you're dead." So you check first to do sure you're not dividing by zero. And then what? The autopilot says, "nullity." Your pacemaker says, "nullity." Yer departed anyways!

JacobI wish my lofty school math teachers had been this open-minded. Making up solutions on the wing would beget seriously helped me in Calculus.

Tom RitchfordUm, you perhaps necessity some editors with a better grasp of mathematics and its history. The specific view of enhancing the number line with a positive and negative infinity is well over a century antique and was neatly formalized as Part of Abraham Robinson's theory of infinitesimals half a century ago. This isn't particularly obscure stuff -- first year University students beget been taught calculus using this method. The "nullity" view appears to live just unpretentious wrong. You can certainly add any attribute you like to delineate 0/0 (though phi is a destitute choice as it already is used to delineate the Golden Ratio). Unfortunately, you can't give this original "nullity" number any sort of consistent behaviour when you add, subtract, multiply or divide by it -- it's more like a attribute sense "put down your pencil now". Mathematics has too had this exact view for centuries now -- the result of this calculation is "undefined". This is what I was taught in primary school many years ago. For Dr. Anderson to pretension that he has solved a problem that has lingered for 1200 years is hubris, unpretentious and simple.

MattI tried to convince a teacher in HS that 4.pi was a number... she didnt buy it. Maybe this guy can approach up with a theory for it to uphold me out!

JBZero divided by zero = nullity? WTF? 0/0 = 1 1/0 = 1u 2/0 = 2u 2u*0 = 2 That makes a lot more sense.

BobWhat is Nullity/Nullity ? What is Nullity X Nullity ? What is Nullity^Nullity ? What is 0^Nullity ?

Vic SnowdenI can finally sleep!

AimeeCan you not stutter "20 divide by zero equals zero leavings 20"? That makes more sense to me.

Ewen MallochSo 0/0 is nullity which can live drawn as a point above or below (or left or birthright presumably) of the number line. Geometrically, this implies it has a length - a distance from 0, similarly to i having a length of 1. So there must exist a value twice as long or twice as far from 0, so 2*nullity (compare with 2i). 2i can live represented as the square root of -4. What can 2*nullity live represented as in terms of the number line? Is it still 0/0? If so, surely you've defined a singularity as every lone points expressed in terms of "nullity" can live represented as 0/0. The references to getting "errors" when computers divide by zero is just destitute programming. Yes, it produces an mistake by the code should resolve that mistake cleanly - by defining it and an action to take. How is that different to a definition of nullity or NaN?

HeIsRightAll you people that discredit this are just jealous fools who wished you thought it up first. So fade back to your hole and sit down and shut up.

KevmanSo, will the IRS allow me to submit a nullity return?

CoolWow..1+1=Unknown

Content FreeYou beget failed to note how assigning a attribute to positive and negative infinity changes anything, other than the student's skill to write the attribute in belt of "undefined".

TokkanjinAnother silly theory: 0/1*1/0(As above) =1/infinity*infinity =1 ohh which is what every lone other numbers are to the power of 0. Therefore according to the above 0/0=1 so nullity=1 therefore according to this you beget reinvented 1

GurrahBeautiful ! Congratulations ! The numbers of variations of an innumerable set of problems might now toil out to become practically possibilites for anything from physics to mechanics. A distinguished great breakthrough - If I had a stutter I would muster it Nobelprize-worthy !

NictitateWhat's Pi in binary?

l0rd_4thl0nBravo to Dr. James Anderson. Your toil is simply excellent, even if these self-professed by view "experts" can't comprehend the consequences of your valuable discovery. I will live following your toil further.

Felix PerssonDid Pythagoras live 1200 years ago?

Suprised Swiss Computer ScientistAhem ... I _think, 0 to the power of 0 is 1, and not Nullity (whatever that's hypothetical to be). This total thing is ridiculous and there could only live one day in the year where I would understand this appearing on the BBC web site, which is April 1.

George CookRead chuck norris's ninja comment. Thanks chuck - elegant and insightful - this "professor" would live much better teaching his calss your way. too - I hope that the year 13 stats remark was not someone in his class.!?

Real simpleso, nullity? ok, on a real computer, if you wanted to prove nullity (or non-trueness), muster it NULL or NIL. x / 0 = NIL there is your nullity birthright there. wha does it solve? nothing, since nullity is itself undefined.

Don PhilipThe mechanics of the theory itself are facile enough to understand as far as he has presented it. However, locating a number off the number line is the problem, and to fully understand what he has done, one would necessity to understand the mathematical justification for being able to consequence so. Otherwise it's a cramped like saying that you've approach up with a original number (we'll muster it snark) that equals the square root of negative 1. Without a proper justification or proof, it's just a word with no meaning. Dr. Anderson needs to do his proof more clear before I can accept this.

Forrest GumpMama always said... Nullity is as nullity does...

KimThis has to live a joke.

A Random Smart personDear sir, trying to net your title in the history books by saying nothing is nothing will not work. You create this highly obstrusted math to try to note something that is to live something it isn't. N/0 = undef for suited reason. Trying to stutter 1/1 = 555555/555555 its upright but it isn't so. suited day.

DaveAPRIL FOOLS! - Oh wait, its December.

Tom Horseonovich ColliganI beget followed this thread with interest, and correspond that perhaps the best forum for exploration of a original theorem is not in a classroom of immature students, but before a curious and critical group of advanced mathematicians. Though there are issues with this original theorem which appear to render it counterfeit when examined in a purely mathematical context, I consequence observe value in exploring the possibilities of "nullity" within the realm of computer science. Tom Horseonovich Colligan Rouse Ball Professor of Mathematics Cambridge University

Alex ZavatoneI don't understand it because I can't observe the video. please exhaust some cross platform video file format like .mp4 so more people can view the video

norwegian guyThis is an antique "solution" to the problem, it has just not been accepted as a solution. Imaginary numbers (numbers which sits outside the conventional number line )has been used for hundred of years in calculating negative square roots and equations that beget no solutions. But its still not a suited solution to a problem, as the calculation is not feasible using "accepted" mathematical methods.

alan r. - math gradI am very interested in reading Dr. Anderson's paper when published. But what strikes me most captivating is that there are so many extremely tough reactions against his idea. Obviously it has struck a chord with a lot of people and that often happens when a long standing view is challenged. (At one point in time not too long ago it was just taken as fact that the sun revolved around the earth. Challenging that view could beget resulted in your execution.) Unless you beget already read his mathematically rigorous theory and proof as would live published in a paper and create a rigorous flaw with it, i contemplate it would live premature and immature to bounce his view or apply to title calling. Mathematicians should beget no intuition to feel threatened by his proposition if indeed it is "so obvious that he is wrong." But it appears that most of the comments are intended to consequence just so after only having read an article written in layman's terms. Number fields are defined by axioms - if he has been able to define a set of elements that adhere to the axioms, then would live nothing mathematically incorrect with his arguments. I beget not seen anywhere where he has stated that nullity lies in the real Number field; thus it does not "break" the arithmetic of numbers most people are intimate with. He is in fact saying that nullity "sits outside the conventional number line." The problem is that it may live very difficult (albeit not impossible) for the impartial person to approach up with a metaphor to uphold them understand nullity. For example, you don't beget to understand the Rational Number bailiwick to know that 1 apple plus 1 and a half apples is 2 and a half apples. People often exhaust this want of understanding to give themselves leave to exhaust the perverse justification: "If I don't understand it, it must live wrong/he must live an idiot." Dr. Anderson has an captivating view and once formally defined then it should live reviewed critically.

A. CarantiI read one of the two papers Dr Anderson co-wrote, and it seems to me that once you net Phi (the "nullity") in an intermediate step of a calculation, you are stuck with it for the rest of the calculation, in the sense that every operation that involves Phi will always give Phi as an answer. So what would you like better, a computer that works for an hour, and then gives you Phi for an answer, or one that after a minute or so tells you "Look, Doc, you just asked me to cipher 0/0: you want me to reserve working for an hour, and then give you Phi as an answer, or perhaps you prefer to reconsider the programme you asked me to run?"

Seiko FlossbergGood idea, because it happens every lone the time that pacemakers divide by zero and desist working. In case you didn't notice, I was being sarcastic.

JamesIf Dr Anderson's axioms are consistent, and more importantly as far as mathematics is concerned, novel, then he deserves congratulations. I don't observe any exhaust for them currently, but that doesn't live substantive there isn't one! Other extensions to the excepted set of numbers were too thought to live useless at the time (I'm thinking of imaginary numbers), but became hugely useful later.

PKAre you actually saying division by 0 is possible? Because writing 0/0 presupposes that division by zero is possible. If so, consider the following: 1*0 = 0, so 0/0 = 1 2*0 = 0, so 0/0 = 2 3*0 = 0, so 0/0 = 3 etc. If division by zero i So does "nullity" = any number I want it to equal?

B1Division is just a short-cut for subtraction; any problem becomes: 'How many times can you subtract x from y?' An the respond to how many times can you pick nothing from something? Is infinity.

Ranjit WassanUnderwhelming story... Why doesn't the BBC cover zero point energy sources such as Stan Mayer's Water Fuel Cell or the Folks in Australia that are driving around their cars running on water. Modern Science is stuffy ans arrogant. If it toil then exhaust it. Maybe the world would live a better belt if they did not beget to rely on Oil! BBC - Bring us HHO gas stories!!

Rick SpivillAnother triumph from the University of Reading's comp sci dept.

Mahesh SooriarachchiI contemplate this is just re-naming the problem to something else... then again, if you really contemplate about the basics of division, the problem of division by zero comes into being because of the view that zero is not really zero, but a really, really minute number. So maybe the solution this problem should live to define zero as being trually zero (ZERO), nothing, zilch, nada! Now if you behold at division this way, lets stutter you beget an apple (thinking of Newton) to live divided among 2 people... each gets half. Now if you divide the apple between ZERO people, what consequence you get? I beleive its the total apple... so dividing by upright zero is the number itself!

Jon BakerProving that NULL exists and giving a cutesy name. Now why did I not dissipate my time doing that??

UndanI was wondering... what would live the result of nullity/nullity ?

Kurt FitznerThe "problem" of a computer with divide-by-zero errors is not a problem, it's a feature. It's not something you necessity to or even want to fix. You could easily design a computer that doesn't beget an mistake in that situation if that's what you want. Replacing the mistake condition with a original attribute accomplishes nothing. The program still has to deal with the issue in order to present a real-world result to the user. A divide-by-zero mistake is the course programs consequence that. It's facile to solve a "problem" when you're the architect of the definition of the problem in the first case. Dr. Anderson first defines a problem: calculators and computers hurl an mistake when you try to divice by zero, and then defines an artificial solution - but the problem was artificial in the first place. We've every lone rush into poorly designed programs that don't exploit divide-by-zero errors properly and crash. This isn't a problem of dividing by zero, this is a problem of a computer program not handling its data properly. We've too every lone rush into programs that attempt to reference a null pointer. By the very reasoning, they could define the remembrance that a "null pointer" points to as some original type of virtual space called "nullspace" (trekies should prize my resistance to the temptation to muster it "subspace"), and muster it valid. do the computer such that reading from "nullspace" always returns a null. Suddenly no programs crash from dereferencing a null pointer any more. It doesn't live substantive that the program is going to now consequence something useful. It probably means it will finish up displaying garbage to the user, hanging in an eternal loop, or branching off to never never land. As far as it goes mathematically, there's nothing you can consequence with nullity on paper that you can't consequence by simply leaving it as (0/0) in the equation. So from either approach (mathematically or from a computer science perspective), it's nonsense. The author's own response to some of the critics (or, I should say, alleged response) doesn't uphold my opinion. Tossing out the names of two other Ph.Ds and offering vague references to undescribed "axioms" built around this original attribute every lone reinforce my view that Doctor Anderson sounds precisely like the character Robert from the movie "Proof".

SteingrimHe's worked his course in an apparantly conventional manner to where 0/0 = 0^0 Okay. Then he assigns "nullity" to both sides. So what ?

ShadowkillerSo wait, let me observe if I understand here. Nullity = 0/0. As the professor showed us, 0=1+(-1). So 0/0 = (1+(-1))/0 = (1/0)+(-1/0) = Infinity + Negative Infinity. As everyone knows, anything minus itself equals 0. So this means Nullity = 0. consequence I win a prize?

JasterSo Dr Anderson replies saying he IS using 1/0 = infinity which is counterfeit (1/x tends to infinity as x tends to 0, but this does not live substantive 1/0 = infinity) If he defines Nullity = 0/0 and Nullity does not uphold with x/0 problems on computers (testing for division by zero is already done and testing for nullity is as easy) then what exhaust is it ... this does not clarify that and neither does his reply on this forum This might live apposite and useful but not to computer science - computers already cope quite well enough ... but what does it allow you to do? this has not been explained?

keshi just read anderson's post. he seems to live using the real projective line and then saying 0/0 is not on the real projective line. and this gets published as original?

BrianIf a computer program divides by zero and crashes, that is not the computer's fault, it's the programmer's fault. It's throwing an exception, and if you don't ensnare the exception, then you're not a very suited programmer. This PhD didn't listen very well in his first year CS course.

fellow anonwow, anon really left alot of messages tearing this guy apart. i wanted to respond to some below comments, but there is no >>1748433373 to click on. However this is /0 GET.

2+2=22This is totally improbable I admire you man =)

Darren McDonaldThis is nonsense, nothing has been solved. Your impartial maths A-Level student would live able observe that. The BBC should feel ashamed for publishing this.

ijif "Let me try to answer..." is really by that "Dr James Anderson", I just can't understand he can train somewhere. The only thing I like here is the "General mistake has occurred" message (Dr Anderson's theory in detail).

EverettI loathe to add to the slew of comments, but I can't desist myself. You can't consequence this to the real line and preserve it's properties. At the fundamental topological level, positive infinity and negative infinity aren't on the criterion number line - it doesn't beget upper or lower bounds. And if you tack on another point "outside" of it, you change the topology. Is that point an open set? Closed? 0/0 isn't a problem that can live "fixed". It's a property of the real line.

DavideLHmmm ...: Inf = 1 / 0 Inf * 0 = 1 [A] Inf * 0 = (1 / 0) * 0 Inf * 0 = (1 / 0) * (0 / 1) Inf * 0 = 0 / 0 Inf * 0 = Nlty [B] By [A] and [B]: Nlty = 1

AyeRoxorNullity is merely a attribute that says "I don't know". Not quite as groundbreaking as it's being made out...

JimMy god that does it P=NP ... it's finally proven.

PatrickNullity may solve the problem of writing 0/0 as 0/0, but doesn't solve the generic problem of dividing by zero. What they necessity is a original sign, not a original number. behold at it this way, if you divide 23 by 0 and net nullity, try multiplying nullity by zero. consequence you net 23 back? No! What consequence you net back? Another nullity? Zero? Where's my 23? Now consider a original sign: '@'. 23/0=@23 -23/0=-@23 @23*0=23 -@23*0=-23 Start looking in the second dimension and observe the number line is not ---, it's -|-

Dr of what?Simple proof that breaks "nullity": y = y y2 = y*y (y-y)(y+y) = y(y-y) &#934;(y+y) = &#934;y [divide by zero] &#934;y + &#934;y = &#934;y 2(&#934;y) = &#934;y 2=1... ?

Mark SkerrittIf you beget 0/0, its undefined, exhaust calculus to net the desired result. This is useless.

chrisI don't know where you guys beget been every lone these years, but math did not just drop into their laps fully formed. It's always been about defining systems that are governed by rules (axioms). As long as your system is internally consistent it is valid. (There are non-Euclidean geometries where triangles can live made from three 90° angles.) Now some consistent systems are more useful than others; if it is upright that Dr. Anderson's system contains the total of criterion arithmetic along with this original definition, then I observe no problem with it. I would live interested in seeing every lone of the axioms defined. remember that for a long time everyone thought 1/0 was impossible to define, but now it is accepted that 1/0 = infinity. This original concept is really not much of a stretch beyond that.

vrochelet me guess, next someone is going to approach out with an 'everything number', if it doesnt exist already, that contains every number [read:every state]. Schroeder's Cat = 'everything'

navim88...really....? step 1. people don't know the respond to a problem step 2. ill title the problem "nullity" step 3. the respond to the problem is "nullity" wow I'm smart.

Martin SpamerI'm a Computer Scientist not a Mathematician and a natural sceptic. However this is captivating because of the symmetry with how null IS handled in Software Enginnering. Null != 0 and is held outside the scale of real numbers. Null is usually represented as \0 which might present a better alternative than a original symbol.

WillAll he's done is do a title for a problem to mask the problem... I don't contemplate it really solves anything.

Kirill A. WoroshilovAnd what does that guy contemplate about L'Hospital's Rule?

Emmanuel D.I am very sceptical about such "theory". First, it is quite confusing, and I don't observe how it can uphold to understand some problem. if 1*nullity = 2*nullity, then nullity/nullity = 1/2 AND nullity/nullity = 2/1. But even worse, 1 = 2*nullity/nullity. So you beget to stutter that nullity/nullity is undefined to clarify this answer. Your transreal arithmetic fails to consequence this, as far as I understood it. Second, since it's still confusing, Iit would beget been better to wait for for mathematical evidence before teaching this extraordinary things to pupils. This is nearly criminal. Next year some other teacher will approach with a theory that says that 2+2 can live equal to 5 for very big values of 2 and minute values of 5. Will he live birthright to train this to pupils before being confronted to his collegues? I contemplate no. Working in this course is just unpretentious dangerous. Science and math needs to live proven before they are taught - that's a basic fact. You too failed to consequence this, and this is criminal imho. Finally, nullity doesn't really uphold when it comes to computers. How will you delineate it (and both infinity and negative infinity) using a 32 bits integer? Or a 64 bit integer for that matter? remember you still beget to succeed the rules of 2-complement arithmetic... That's going to live quite hard. I guess the solution is to give them some special values, and to hardwire the calculus in the ALU - this is not very efficient imo. I don't want to stutter that the theory is some random bullshit (I'm inclined to contemplate that a representation of these numbers is quite important), but I'd wait for better proofs - ie not proofs that are backed up with the IEEE FP standard.

SkuffIm no mathmatician (infact i struggle to spell it). So im not really sure about every lone this 0 stuff. But i contemplate the intuition math exists is to toil things out, probably starting at some local shop and adding beads or something etc...il trade one loaf for two fo these or what ever. So in my ignorance I behold at it simply, such as: stutter they beget One cake. They beget 5 people. The cake weight 500g. So each person (if divided equally) gets 100g of cake each. So, if theres 1 person, they net the total cake, 500g. So, if there arent any people to divide the cake between, doesn't that live substantive that 500g is still left? Crude, Im sure. But, surely thats right? 500/0 = 500? I guess this might live Part of the problem, in maths this just cant work. I consequence find that there seems to live a few holes in the hole mathematical system and they seem hell bent on trying to reserve it as the birthright course to consequence things. Its takes someone to try and prove other systems, it seems in todays world they appear pleased to exhaust old(ish, perhaps, although improved over time) methods that yes, beget been tried and tested, but may live not entirely correct. If a tree falls in a wood and no ones heres it, does it do a sound. Yes, of course it does, dont require such daft questions ;)

YabaTheWhatThere is absolutely no necessity for this imaginary value. First off, any number to the power of zero is one. Why? Let's stutter N is a number, and R is some random number. RxN^0 is interpreted as, "Multiply R by N zero times," or more generally, "Multiply R by... wait, no, nevermind, just leave R alone." Next, let's address the concept of 0/0, or zero divided by itself. The simplest respond is that any number divided by itself is one. Obviously computers beget a problem with this concept, so let's approach it from a more many-sided standpoint. Computers beget rigor dividing by zero, because 1/0 is infinite, and computers only deal with finite numbers. That's the problem designers would necessity to fix. Instead of treating numbers as finite values, tack on an infinity tracker. Let's exhaust oo to delineate infinity, since I'm writing in a text box. The basic problem is that 1/0 = oo. In finite mathematics, that causes an error. However, 1 in a finite system is actually 1 not multiplied by any infinites (or not divided by zero). They could stutter that finite 1 is 1 multiplied by no infinites, or "one with zero infinites" as a shorthand version. Now divide it by zero. The result is one with one infinite. Now divide 1 by this result, and you net 1 (from 1/1=1) with -1 infinites (1/oo). Divide this number by zero, or multiply it by oo, and you're back to 1 with 0 infinites, or finite 1. To divide by zero at any time implies that zero is, in fact, not an absolute value, but simply an infinitesimal value; it is so minute that it is regarded as nothing. This, from the perspective above, would live called, "one with negative one infinites." They could, of course, multiply it by itself to net the value, "one with negative two infinites." Multiply this by oo, or one with one infinite, and you're back to one with negative one infinites. Multiply by oo again, and you're at one with no infinites, or finite 1. Taking the concept a step further, consider the simple equation (x^2)-(2x)+1=(y^2). In finite math, that's a simple problem to resolve. What about if x = oo? The respond is that it's still the exact very problem. The answer, y=x-1, still applies. Writing out the equations, we'd beget one with two infinites minus two with one eternal plus one with zero infinites equals the square of "y", resolving to "y" equals 1 with one eternal minus 1 with no infinites. So what's oo^oo? Guess you'd necessity to tack on a second infinity counter to the number at that point. While I wouldn't anticipate a simple hand calculator to exploit this problem, any scientific calculator designed to exploit the square root of negative one should live able to exploit infinites in this manner. Getting back to the total issue of "nullity", it's basically useless. Nullity basically means, "One multiplied by some finite numbers I was too distracted to track." If accepted by the mathematical community, it could easily live used to prove that 1=2, or a variety of other nonsense. [Gyeh. There are too many replies to this discussion already. excuse me if someone has already said what I just said. It always seemed to me like a fairly obvious solution.]

AnonI'm studying in the Reading University Mathematics department. I would like to point out that this guy is not a mathematician and works in the computer science department. Hence any theories that he proposes are nothing to consequence with the mathematics department.

David MellorWhy such skepticism? I'll pot people would beget said the very about the square root of minus one, and behold how useful that is now (really!).

BlackTiger... Quite strange. If you are dividing something by 4 it means "divide in 4 pieces", isn't it? Ok. What is result of "dividing in 0 pieces"? Just nothing. What's wrong with it?

DecipherInventing a original term to deal with it, is not really solving it, is it?

AimeeTry a different symbol, sir! That one your using equals 1.618 and it's one of my favourite numbers!

MaryMy understanding of the real numbers is that they don't actually end. So how can infinity beget a value? That would live substantive the finish of the real numbers, which is not possible.

NullityI beget nothing to say.

Albert EinsteinWhat is nullity divided by nullity? Negative infinullity?

ConfusedIf this problem hasn't been solved for 1200 years, who solved it 1200 years ago?

PythagorasIf the definition of infinity (positive) is 1/0 then is 2/0 not two times infinity? This would live a larger infinity by the math rules that I know. This concept can live extracted an infinitum. As a result, 1/0(1/0) is an eternal infinity, too know as an absurdity. Does this do any sense? Infinity is eternal by definition and therefore nothing is larger. Maybe, just maybe Mr. Anderson is 1/0 nuts. That's it, the man is off his blinking rocker. Now for there real issues of life - just how many angels can meet on the head of a pin?

D.V.1. if you read his axioms you will realise that "nullity" is what humans beget been calling "undefined" for 1200 years. The axioms are identical. He just renamed the word. 2. if your heart pacemaker divides by zero you are NOT dead. there are things called watchdog timers that reset microcontrollers when things like that happen. 3. creating an remonstrate out of "undefined", called "nullity", that behaves identically to what they beget always known as "undefined", does not uphold computers or mathematics any.

KhojiDr James Anderson wrote: "It is just an arithmetical fact that 1/0 is the biggest number there is. " Rubbish. That's about as meaningful as saying that an orange divided by an apple is a pear. 1 is a quantity. 0 is the want of a quantity. Using symbols from the very numerical system for both of them creates the intellectual illusion that they are both numbers, but they are not. Thus, the entire nullity edifice collapses upon itself.

Beender DundatMy theorem: any number (includig zero) devided by itself is 1, ex. 1/1=1, 123/123=1 and 0/0 = 1 and infinity/infinity = 1. Also, any number (including zero) to the power of 0 is 1. Anything devided by zero is infinity (positive or negative, depending on its sign). immaculate and simple.

UnnessecaryStudentEhhmm... Thats extraordinary - To declare a original "number"/"letter". I'm not pleased about this solution. I'm sorry.

JaapHi, If this problem is 1200 year old, then what does Pythagoras beget to consequence with it?? And as physicist I did not observe any original math here.

AnonymousAny Java programmer will live able to observe the similarity to Double.NaN (Not a Number) constant. This was introduced by Sun atleast in 1996, could beget been earlier if done in other programming languages too. The only extension here seems to live that its being brought into the non-programmer world.

Brian MatthewsHere's why 'nullity' doesn't work: WHat is nullity divided by nullity? Well, it's 1, isn't it? On the other hand, this is too equal to (0/0)/(0/0), which by simple maipulation of fractions is equal to 0/0, which is nullity. So nullity equal 1. Nonsense. QED.

SekkyGuys, this sage is in no course analogous to complicated numbers. complicated numbers are no more or less artifical than the negative integers or rational numbers, they're every lone just extensions to provide a superset. They are in no course like what is being suggested here, which by the way, is an embaressing regurgitation of absolutely nothing. Ignore every lone research papers from the University of Reading.

Navid ZamaniI KNEW it! I KNEW it the total TIME! Never since i first heard that there is an "exception" to every lone math, when using zero, i felt very tough that this is wrong. like a glitch in the matrix or 2+2=5... You know it. I searched for solutions to it. But they mostly went with "something / zero = infinity_n" where n held the information about "something", so by muliplicating "infinity_n * zero" you would net "something" back. Worked quite well, but there were problems with it.... (that i can't remember for now) I'm REALLY pleased this happened! So i finally can recommend my ex-teachers that *I* were birthright every lone the time! THANK YOU MR.... Anderson...? Oh... my.... GOD... I's you Neo! You solved the glitches! :D

MikaelSo, how does this relate to the theory of algebraic wheels; which as I remember it too deal with 0/0 by extending the extended reals to comprise this as a original formal element?

Three lofty School Math Teachers Mr. Gagliardo, Mr.This is not something original under the sun. 0/0 is undefined; but it can live too live considered indeterminant because it can live any value. 0/0 could, for example, live 7 because 7 x 0 = 0. It could too live -41, .2, etc. Calling it nullity is just a bit too cute. However it gave us something to contemplate about.

Kyle BurtonI'm sorry, but there isn't exception handling in integer division

Funny ThatThis has to live a jest of some sort! Some distinguished comments below though: Bob:"The program wont crash, but the plane sure as hell will." :0)

Dr Richard Daniel HillThis man is a charlatan and a crank

&#12521;&#12452;&#12488;0/0 = Nullity? Next thing they know, he will recommend us that .9~ =/= 1.

nullity.complex: defn: people with nothing to consequence bIt does amaze me that so many smart people feel the necessity to shoot down another mans ideas....whether snide or good. Obviously cramped else to consequence with their null lives. Its facile to live a critic. And nearly every commentator has approach up with the solution at some stage in their immature lives. One things missing...why did these people consequence nothing with their original ideas? Even distinguished minds had solved problems in the past, but gained no recognition for it because one has to observe opportunity/value in such solutions. From my point of view: if i pick 10/5 = 2 and transform it to 5*2 = 10 then I would anticipate that 1/0 = ? could live rewritten as 0*? = 1 but multiply by 0 gives you 0. This is what we've always been thought. They can too never recommend if 1/0 is negative infinity or positive infinity yet both are possible. NULL is used in computer programming to define live substantive nothing/empty/undefined. Its allows checking for the actuality of something of interest. Comes from the latin word nullus sense "not any" Is it not feasible the professor is trying to clarify this theory through algebra..... I cannot view the video so I consequence not know. And so what if its been discovered. I'm sure its a helpful approach to teaching this stuff.

JCAI phenomenon how Dr. Anderson handles (a real number)+(infinity) - (another number)-(infinity). Since his infinity lies where it does, how does he exploit it?

prober8if: 0/0 = Ø so: 0/Ø = 0 then: Ø = 1 ??? nullity = unity ???

Adam BraunExpress it as binary.

AnonEvery bailiwick has a nullity. That's basic abstract algebra. One should live wary of people defining things conveniently without rationale or proof - what you've got there is just numerical masturbation. Avoid mathematical sensationalism at every lone costs!

MattI came up with the very solution years ago except I used the attribute "Doh!".

Thom HowesSimple question, if the numerator and the denominator both approached 0 at the very rate, wouldn't the result always live 1?

SimonIt's upright that dividing by zero does occasions an mistake in programing, but any programer that has every written a program more complicated than "Hello World" (Tradtionally the first program you ever write), will know to trap the mistake before it occurs. So it can live dealt with gracfully (i.e. assigning a defaul value instead), rather than crashing. Any of the modern or remonstrate orientated programing language will beget expection handling built into the it for just this sort of problem. As a computer scientist, I would beget hoped Dr Anderson would know better.

Mutant RobSo has he vetted this view in reputable maths journals among other mathematicians, or is he using his power as a school teacher to foist quack ideas on his students, much like "rational trigonometry"?

ChrisNewton? Fool. Pythagoras? Useless. Anderson? God. consume your heart out, creators of mathematics as they know it!

The MoleSo: Ships and planes unexplainedly evaporate in the Atlantic. Let's assume there's a location which lies outside the everyday space/time line and give it a name. Now the disappearances are every lone explained just by saying "Bermuda Triangle".

LJLIt's been a long time since my Advanced Theory classes, but doesn't a number lying OFF the number line violate the axiom of Completeness? I find it hard to believe Dr Anderson would beget simply overlooked the most basic axiom in advanced mathematics, but that's exactly what he appears to live doing. Before contradicting the exhaust of the term number here, let's kisser it, anything used to delineate a value is a number, even if you muster it a non-number. I beget a problem wrapping my brain around a value divided by a value producing a non-value. One might as well stutter 6+10 = a dog. This is violating - or rewriting if you prefer - a number of concepts that the vast majority of mathematics, from simple computation to advanced theory - relies on. I won't fade so far as to exhaust the derogatory terms presented by other commenters, but I certainly contemplate dropping this from the drawing board to a schoolroom without peer review and generic acceptance is irresponsible at the least. I consequence realize that the particular problem of division by zero is a particularly anomalous one, so I can understand the unorthodox approach, but there are times when either infinity, negative infinity, zero, or 1 mind to "fit" human intuition - which they every lone know is not always even close, but for real! I consequence contemplate there's a course to exploit this, but I contemplate it's maybe just a cramped more involved than "Hey! Let's do up a original (non)number!"

GooseAnyone know of a credit card with this kindly of interest rate??

No bodyTake the pairs (a,b) of real numbers. Two pairs (a,b) and (c,d) are "equivalent" if there exists a non-zero real number x such that c=a*x and d=b*x. This is an equivalence relation. Let "a/b" denote the class of (a,b). Let the "product" of "a/b" and "c/d" live defined as the class of (a*c, b*d). Let "nullity" live the class of (0,0). Is there something more in the nullity theory?

Mark JohnsonCan they invent some original letters to the alphabet as well. Sorry but "making up" a original number does not solve divide by 0. The respond should approach out as an mistake and thats the course it should stay.

its meI too beget solved an antique age problem. The sense of life which I muster Liath. It is quite simple now that they understand that Liath happens between Life and Death ;)

Nathan GerberSo ok if this is solved, just how consequence I pick this original value and continue solving a problem? Basically every lone this is doing is taking away a "divide by zero" mistake and replacing it with a "nullity" or "negative infinity to positive infinity" error.

QrizWow...some loooooong explanations there. 0 is something they made up. dividing by 0 (for example, dividing 9 into groups of 0) would net you infinity. So you start dealing with kinds of infinity, which is too a concept, not a definable value. Zero and infinity are artificial, and they uphold us delineate and toil through problems. like someone said down there, math is every lone definition. There isn't a "right" respond unless it fits these definitions.

DaveHyperbole. I had to note more proof in grade 5 - but I suspect this quack has no proof.

Stephen Leary0/0 is Not A Number. This is well defined in computing science/Maths etc. "Nullity" is just a redefinition of this and has been around for years.

CharlesNice joke. But you can't deliver a quantity on Nothing, that should live just about Obvious to everyone around here

Carolus HolmanIf I pick an Orange, and divide it by Noting or 0 or don't prick it, I still beget a total orange. So in my layman brain 1 orange divided by nothing is still an orange. I am surprised that the British are so gullible, but then again, I am British.

JoeDr Anderson has done nothing but add a original notation that was not needed. His definition of 1/0 as Omega is flawed, as there are larger eternal numbers. Modern computer programmers exhaust exception handling to manage the "divide by zero" error, and this "new" concept adds nothing to that science.

Cracked out winoDude, Nullity RULZ!!!!1111@#$Professor smart guy for preZ! Stuart hard ManThis guy needs to harden up. Seriously Plus Lee and Bag consequence some work! Story ProblemThere are twenty apples in a bag. Neither Rick, Jane, Sam or Betty want any of the apples. How many apples does each person get? 20/0 = nullity Each person gets nullity apples. Bored of EducationSorry, this guy is a fool. Nullity is not a real number, and you cannot gain it from dividing by zero BECAUSE YOU CANNOT EVER DIVIDE BY ZERO TO start WITH!!! ummmummm real player? are you serious? MikeThis is just stupid, nothing has changed, they just now beget a title for the no non-value that results. You may as well muster it mistake so that at least the calculators are still right C R HulcherZero is a belt holder, never was a "number"!!!!! JoeThis is not unlike astrophysicists who, when their numbers don't work, just theorized something they muster "dark matter" which does nothing but fill in the gaps in their equations. ChocoSo many comments here from the computer programmers' camp - how many of you can honestly stutter the computer languages from which you draw your examples are mathematically rigorous? When was the terminal time a mathematics prof wrote "Type mismatch" on the blackboard? A bit of reading up on e.g. Peano arithmetic is needed before challenging Dr Anderson's working. de GraafSo... does this relent an respond for the Le=orentz-Fitzgerald equation (that yields a division by zero when the velocity of an remonstrate matches that of light)? TofuHmmm.... I beget an insolvable problem. I KNOW! I'll just do up a brand original irrational expression and pretension that that is the answer! His step-by-step "detailed" instance doesn't solve 0/0. He just gives a convenient placeholder instead of an mistake message. too how can he muster "nullity" a number if it doesn't topple on the number line? Heck I could stutter an apple is a number now and exhaust his very logic to validate my theorem. Gunnar GregerDivide infinity by infinity: Infinity/infinity=0, or is it? contemplate about it. 0/0=Infinity or is it 1? The solutiuon is hidden in infinity? Peter Tettweiler, Hamburg, Germanyto live honest: no! Shady TarekIs there any practical problems solved with this ? I live substantive ok there's a original number now what does it consequence ! Matt FletcherExtending the bailiwick of number by adding special elements (e.g. infinity) is a basic and picayune operation in alegbra. There is absolutely nothing original here at all. The BBC should only report scientific advances published in peer-reviewed journals. Anderson's toil seems only to live released via his personal webpage where his paper supposedly demonstrates "the possibility of division by zero and challenges the reader to accept it". Not the accustomed wording for a technical paper with something genuine to say. please desist giving this nut free publicity. DavidJust consequence what I consequence - when in doubt what consequence you net if you multiple 6 by 9? 42. (And for those who don't observe the connection - 6*9(base 13) does indeed equal 42 :) Thank you to the late distinguished Douglas Admas for that Gem. 1/0 or 0/0 will remain NaN for a long time yet. Until C supports nullity - no computer will stand a chance of understanding the concept at the basic operating system level. Alexander RozmanHow does making up a original attribute solve the problem of computers diving by zero? Just how does this theory insinuate encoding nullity in binary or performing arithmetic operation on it? TRexThis is great, but I don't net it, can you write a job aid for it? Morten V ChristiansenI am not sure what Dr. Anderson has done, but in principle the view is not problematical. Several non-standard interpretations of number theory exist, some with eternal sets of "alternate zeroes" or infinitissimals. They are provably as consistent as criterion number theory. This is no different from non-standard set theory or non-euclidian geometry. If Dr. Anderson has created an proved the consistency of such a system, which is accessible enough to live understood by school children, I contemplate that is a very nice accomplishment. It does not revolutionize mathematics, but it is very nice work. AlphaAXPThis theory looks itself a lot like the own result it referes to: a nulity. "A" quantity, even if abstract, can live defined, not "Any" quantity. amusement but not original. math already owns a attribute for "Any value": it's a capital "A"O upside down. Dr. OH RLY ObviousTo: Dr. Obvious, If you times a irrational number a rational, you net a irrational. RouDyThe 2nd step before the latest is counterfeit (1/0 is impossible). And 0/0 is impossible too. (sorry for my snide english, i'm french) Tim PozzaWill the original number allow us to cipher when infinity touches itself in space and in time? ZipNot a Number is basically like a workaround to reserve an application from crashing a virtual software engine. That's about it. It's not a mathematical proof of anything. Basically, every lone he did is to submit a fashion that can live used in divide by zero situations, that's it. There's no intuition for almost every lone of these chest thumping replies. It is true, though, that this probably isn't going to magically fix software glitches of any kindly in modern managed code. Maybe it would allow lower even code (assembler, c, etc.) to not beget to ensnare divide by zero errors on systems with updated firmware that handles the concept of "nullity". That's about it though. The problem then becomes backward compatibility. ;) Michael ClaytonQuoting the Dr. Anderson "It is just an arithmetical fact that 1/0 is the biggest number there is.". That is unpretentious RUBBISH. Patently FALSE. Here's the proof: 2/0 > 1/0 SebHaving 0/0 as undefined is useful as you can't exhaust it. If you define it as a attribute people exhaust it in algebra and you finish up in every lone kinds of 1=2 kinds of problems, throwing out an mistake from your calculator is a suited mark you made a mistake and should fade back and fix it. JMSI'm relieved to observe that his PhD wasn't in mathematics. That said, the respect that the title "Doctor" brings should live used wisely, and certainly not in misinforming the generic public, let lonesome vulnerable children. This made me very ireful indeed, to stutter the least. Angrier still, when I read his papers on "transreal analysis". Again, I'm cheerful that these won't live published in any respectable mathematical journals. What he has done is not mathematics; it is more closely related to the bailiwick of linguistics: don't beget a word for something? Let's do one up and then exhaust it to clarify the very word. He has decided that the problem of dividing by zero can live solved by saying that if it could live solved, its respond would live "nullity". Ignoring the fact that nullity then breaks most commutative laws, he has not used nullity as a fashion for solving any real problems. Some beget said that his "work" is analogous to the discovery of the imaginary number i (the square root of -1). However, i is useful in solving many mathematical and real-world problems; nullity certainly is not. His papers pretension to invent a original profile of arithmetic that allows the exhaust of his original number, but in reality they simply add axioms to the existing set so that he gets around the problems thrown up by nullity. Furthermore, he envisages the computers of the future using his original profile of arithmetic so that the "NaN" mistake is replaced by "nullity". How does that solve the problem? Even if the computer then knows how to exhaust it in equations, it won't give any reasonable answers since, by his own calculations, any equation involving nullity has an eternal number of solutions. How dare he masquerade as a mathematician? How dare he dissipate valuable research grants on a something so useless: something that, unlike upright mathematics, has no scientific, philosophical or practical value? I am pleased to observe that there are an overwhelming number of comments on this page ridiculing his toil - most of these people probably beget less education than he but they can easily spot the fallacies in his utterly ludicrous, crackpot theory. cies breijs"-Inf" and "Inf" are no numbers, so "Nullity" is not a number ("NaN") aswell. They could do a dissimilarity between different "NaN"'s and muster them "-Inf", "Inf" and "Nullity", but will this do sense? They they live able to consequence somehtings that was previously undoable (like complicated numbers enable us to do)? I don't contemplate so: NaN + 1 = NaN NaN * 2 = NaN this hold upright for any NaN, so this renders them useless. WalemfrickGreat work! If nullity extends from negative infinity through zero to positive infinity then it is a valid respond for any problem not just this one! 1+4 = NULLITY!, the root of 123786476362783456734 = NULLITY! If this gets accepted nobody has an excuse for scoring less than 100% in Mathematics ever again, sorry NULLITY%. All this is very usefullPerspex machine: VII. The universal perspex machine James A. D. W. Anderson The Univ. of Reading (United Kingdom) (published online Jan. 15, 2006) The perspex machine arose from the unification of projective geometry with the Turing machine. It uses a total arithmetic, called transreal arithmetic, that contains real arithmetic and allows division by zero. Transreal arithmetic is redefined here. The original arithmetic has both a positive and a negative infinity which equivocate at the extremes of the number line, and a number nullity that lies off the number line. They prove that nullity, 0/0, is a number. Hence a number may beget one of four signs: negative, zero, positive, or nullity. It is, therefore, impossible to encode the mark of a number in one bit, as floating-point arithmetic attempts to do, resulting in the rigor of having both positive and negative zeros and NaNs. Transrational arithmetic is consistent with Cantor arithmetic. In an extension to real arithmetic, the product of zero, an infinity, or nullity with its reciprocal is nullity, not unity. This avoids the accustomed contradictions that succeed from allowing division by zero. Transreal arithmetic has a fixed algebraic structure and does not admit options as IEEE, floating-point arithmetic does. Most significantly, nullity has a simple semantics that is related to zero. Zero means "no value" and nullity means "no information." They bicker that nullity is as useful to a manufactured computer as zero is to a human computer. The perspex machine is intended to proffer one solution to the mind-body problem by showing how the computable aspects of mind and, perhaps, the total of mind relates to the geometrical aspects of carcass and, perhaps, the total of body. They review some of Turing's writings and note that he held the view that his machine has spatial properties. In particular, that it has the property of being a 7D lattice of compact spaces. Thus, they read Turing as believing that his machine relates computation to geometrical bodies. They simplify the perspex machine by substituting an augmented Euclidean geometry for projective geometry. This leads to a general-linear perspex-machine which is very much easier to program than the original perspex-machine. They then note how to map the total of perspex space into a unit cube. This allows us to construct a fractal of perspex machines with the cardinality of a real-numbered line or space. This fractal is the universal perspex machine. It can solve, in unit time, the halting problem for itself and for every lone perspex machines instantiated in real-numbered space, including every lone Turing machines. They cite an experiment that has been proposed to test the physical reality of the perspex machine's model of time, but they do no pretension that the physical universe works this course or that it has the cardinality of the perspex machine. They leave it that the perspex machine provides an upper bound on the computational properties of physical things, including manufactured computers and biological organisms, that beget a cardinality no greater than the real-number line. ©2006 COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal exhaust only. MattTo me, it looks like the respond is still the very as it has been for the past 1200 years, he's just decided to draw a squiggle at the finish claiming its the attribute for 'nullity' Gunnar GregerDivide infinity with infinity:infinity/infinity=0 or is it zero?Think about it. Richard Bremner, Aberdeen*Announcement* I beget solved the problem of what is North of the North Pole, it's called Northity. Everyone rejoince. mikeWasn't this article prepared for 04.01.2007 ? Michael McGuireThe man is a crank on the even of the "squaring the circle" crowd. The accepted value of 0/0 is undefined for several suited reasons that anyone with an understanding of topology or even basic calculus should understand. Replacing 0/0 with a special attribute would actually create more problems than it would fix. I recommend a quick behold into the works of Cantor and/or Komologorov for anyone who is interested into modern theories of zero and infinity. Wayne SmallmanAm I the only one to totally underwealmed by this original theory of nothingness? If every lone he's doing is making up a original non-number, I'm hardly surprised by him solving this problem. Almost any problem can live solved by just making stuff up to meet the problem. Some peer review might live more telling... HONKHURFEY DURFEY baby, congrats on coming up with a cute original title for an already proven concept. There isn't anything original here except a silly title and a washed up professor. Dr James AndersonLet me try to respond the comments posted above. I beget defined a original number, nullity = 0/0. I used a symbol, capital phi, to denote that number. The attribute I exhaust is irrelevant, what matters is the definition of the number. I’ll stutter a bit more about this number in a moment, but first let’s net clear what they are talking about. I too defined infinity as 1/0 and minus infinity as -1/0. This is consistent with dividing a non-zero number by ever smaller numbers approaching zero. The geometry of this arrangement is shown in the video. The number line stretches from minus infinity to plus infinity. It does not wrap around into a loop, it does not identify positive and negative infinities as opposite poles in a projective geometry (though it is feasible to consequence that if you want to). The geometry is exactly as shown in the video. The number line stretches every lone the course from minus infinity to plus infinity in a straight line. The original number, nullity, lies off the number line. I drew it above zero, but it can live drawn anywhere that is not on the line. Its geometry can live understood in the very course that the number i, the square root of minus one, can live understood. every lone of its algebraic properties can live drawn as pictures in co-ordinate geometry. Some people exhaust j to bespeak the square root of minus one. The attribute does not matter, what matters is the definition of the number. Once I understood the geometrical picture of the original numbers and understood how to operate on them as fractions, using pencil and paper methods, I wrote the total lot down as ratiocinative rules or axioms. Dr. Andrew Adams from Reading University and Dr Norbert Voelker from Essex University helped me develop the axioms. Norbert translated the axioms into higher order logic and used a computer to prove that they are consistent. The axioms accommodate the total of criterion arithmetic. This is very important, it means that anything that can live calculated using criterion mathematics can still live calculated, but now it is feasible to cipher other things as well. I’ll stutter a bit more about this later, but birthright now let’s observe why nullity is a number. There are many ways to contemplate about numbers (and I exhaust whichever course is convenient at the time), but one of the simplest is to stutter that a number is anything that obeys every lone of the axioms of arithmetic. Therefore, nullity = 0/0, infinity = 1/0, and minus infinity = -1/0 are every lone numbers because they obey every lone of the axioms of my original arithmetic. I contemplate the world has settled on oo as a attribute for infinity, though aleph and omega are too used for different kinds of infinity. If you want to rush a competition to find a better attribute than capital phi for nullity then fade ahead. If it’s a nice attribute I will exhaust it in my scientific papers. In my axiomatisation it is defined that infinity is greater than zero. From this it follows that infinity is greater than every lone numbers. I’ll deliver a proof at the finish of this message, but let’s live clear on what this means. The property of being infinitely Big follows from the fact that a positive number is divided by zero. It is not necessary to define infinitely Big by any other means. It is not necessary to exhaust calculus or set theory to define infinitely big. It is not necessary to exhaust any philosophical concept of bigness. It is just an arithmetical fact that 1/0 is the biggest number there is. As I said, there are various kinds of infinity. It is feasible to add these to the number line. They are every lone smaller than 1/0. In some areas of mathematics a biggest infinity is defined according to the axioms of that area. Several areas of mathematics exhaust the attribute capital omega to denote the biggest infinity. Its properties depend on the axioms in exhaust so they can vary from belt to belt of mathematics. My infinity shares the property of being the biggest infinity, so you can exhaust capital omega as a attribute for it if you want to, but the properties of my biggest infinity succeed from the properties of my arithmetic and not from anything else. Some areas of mathematics define infinitely minute num Tormod HMath is every lone about definition, and making consistent roules to succeed in every situation. to pretension that a conditional statement in computer code is fixing it; is just ignorance. with a math theorem defining how to exploit this situations can help a lot. it is valuable to understand that math is quite different than computer calculations; like with diffenecials, it is feasible to consequence "calculations", but with constraints. if you wreck the constraints you outside conventional math and you are responible for you results. With a replete proven theorem around x/0 they can change computer science too. they just necessity CPU-core suport, and/or define som vector rooms. Major leaps in science history is done by changing the perseption, not claiming that they can cope with it as it is. like the theroy of relativity. ( sorry for the spelling errors. Dyslectic, but not brainless :-) MIchael ChizmarI could not open the video so I consequence not know if this is relevant, but is there there a proof upon the definition of nullity? Or, is this just a rewording of what is already known, like (a previous poster stated) NaN? RenAwww I solved it years ago but didn't contemplate to publish it.. 1/0 = WTF? As you can see, my While upright Float is another word undefined, and the Float lets us know it's a fractional number. Toshke from SerbiaThis is totally dull like every lone similar proofs. Of course it didn't prove anything, he just created a original number, and very that number can live anything, from -inf to +inf. It is not going to uphold any calculations. destitute children, at age of ten, they are being taught of infinity, they should consequence it in lofty school. And this 'nullity' :( Forget it! @ FredI correspond how consequence you repersent Nullity in binary or even hex. The other problem is he didnt even solve the equation he just made up a original entity to provide a solution.. and nullity has always existed its called NULL so in essence he has just renamed the solution. Dave GowerThis is, indeed, rather sad. 0/0 can live defined if a function that limits to it (such as sin(x)/x) is well defined and continuous. anything else, as mentioned above is simply NaN. They're not defined and probably never will be. The proof is diabolical. 0/0 = -0- therefore 0/0 = -0-. Yikes. ytillunIf the airplane divides by zero, my pacemaker crashes :-) or, the pilot has to deal with "we are nullity meters from the ground. Press any key to crash now, or wait for nullity minutes for an auto-crash" How I wish my bank divided my$1 equipoise by zero and told me that I beget eternal money ;-)

ComputingProfessorUm, this is nothing new. They beget the concept of nan (not a number) and even consequence arithmetic with it - any time one of the operands is nan, the result is nan. Fits nicely. So this is just a original title for something that has been around for a while.

van de WeertIn my days as a student they talked about this very problem and defined a solution to it. They called that number "van de Weert", in reference to a much disliked teacher, they had loads of fun with it. And now this .... teacher tells his students this drunk ass talk of us is upright only using a different name? I muster it cool, but I doubt any grave mathematician is going to pick it seriously.

RobThe solution contains 0/1 x 1/0. But his definition states that 1/0 is positive infinity. So it's 0/1 x infinity. But they every lone know that 0/1 = 0 and 0 x 'anything' = 0. So the solution is 0. Is it really necessary to 'make up' a original number? The verity is that he's trying to change the rules. 1/0 is NOT positive infinity! It is well understood that 1/0 is 'undefined'. I commiseration his students.

Brian K.Yes, at first i thought, "pretty cool", but after reading these comments, altho many are a lot meaner than they necessity to be, i consequence observe now that no problem was really solved here. I mean, if you're depending on flight systems software, you're going to beget to ensnare a "nullity error" just as much as you would a "divide by zero" error. How would nullity propagate thru the rest of your algorithm??? clarify that and maybe i'll revise my opinion.

Tasty WheatIf any number divided by zero equals nullity, then what does any number divided by nullity equals to? Divide by nullity error? :)

Blast RadiusThe IEEE criterion already defines 0/0 as NaN, which seems adequate enough. Nullity solves nothing and is simply an arbitrary designator that this professor invented. Unless "nullity" can live used in existing mathematical equations usefully, it is entirely useless. Bob has it redress when stating the uselessness of this non-number.

JohnComputers CAN divide by zero, if they exhaust IEE754 binary floating-point arithmetic (which practically every computer does). x/0 is positive infinity for positive x, negative infinity for negative x, and NaN (not a number) for 0/0.

Lumocolour O'ShaugnessyWill this original fangled contraption uphold me net a bigger slice of a shared pizza?

MikeI already solved this problem a long time ago. The respond is 0 AND whatever the numerator is. Where's my Nobel Prize?

CCMathematicians muster that compactification of the real line, nothing new!

Ibzno phenomenon i always flunked in maths!

a slightly less incompetent mathematicianTake a class on real analysis or measure theory. They construct algebras that can exploit division by zero every lone the time. Dr Anderson? This "new theory" is decades old. I learned it as an undergrad, from professors who learned it as undergrads. And it definitely isn't yours.

Dr DubeyActually, some simple mathematicians had thought of thing quite some time ago (Sometime geometricts in the 19th century I believe).

freak guythis is crazy..if this is passed by the international community then let me submit a theory defining infinity upon infinity as "ellipsis"..

JDHe may live in the computer science department but he appears to live completely unlearned of modern safety critical software techniques. An auto pilot will not "stop working" if it tries to divide by zero, the software will ensnare the condition and try to consequence something sensible.

olLol! Thats just a nice joke! :-) Of course, the "nullity" number is known for a long time (it is usually called "undef") in most programming languages. The amusing thing is to contemplate that people at the BBC buy this!!! :-)))

XpucmoWhat I find useful in his view is that the original number could do it easier and more criterion in programming languages to process results/events which are currently handled by exceptions. Plus it is always easier to exhaust a term "XYZ" than "the event which occurs when you consequence this and this with that and that" - I contemplate this is called abstraction ;) Also, the very fact that this theory provokes such a furious reaction and polarized opinions means that it IS a original idea.

Ngrh8rWe beget a title for this "nullity" and beget had such a title for years. That title is NaN. Learn it well, Anderson. You are no inventor, you are not heralding a brilliant and original mathematical theorem. You are simply giving a original title to something folks from the computer camp beget known for years.

noragree with u Caska might uphold the computer programing and could live captivating there.but for mathamatics not much uphold lol

a uk college studentWhats this guy thinking? First of every lone he thinks hes solved one of the most difficult problems ever, doesn't he contemplate that any mathmatician over the past however many years has thought 'hmmm lets just do up a word for this and it'll every lone fade away' Honestly like someone down the comments list has stated how is this to live represented in binary? I feel dreadfully sorry for the kids being taught this, many people in my previous math classes and I beget said why not just do up a word for it; it doesn't work!

Tomek PerlakWell, the concept itself seems appealing - it's just a original symbol. Just like there isn't "really" an 'infinity' - there isn't "really" a 'nullity' - but it helps to clarify something. (Does it?) I would kindly disagree with Hubert J. - IMHO, there is not really a mistake in this train of thought - please, notice that this original attribute is used to "simplify" the zero-to-the-power-of-zero expression. Merely that. Anyways - I'm kindly of a curious about some other expressions - can the 'nullity' live used in, say: -0- + 12 = ... ? -0- * 3 = ... ? Or are they talking here about a completely original set of numbers, almost like with the complicated numbers?

Johan Krüger-HaglertThis isn't news, and it beget probably been solved long ago. Java for instance sets a NaN-flag when you divide by zero, NaN standing for Not a Number. Afterwards you can easily check for such cases and handled them in whatever course you contemplate is appropriate, the valuable factor is that the program keeps on running instead of crashing.

!!!defining a original attribute doesnt do up a theory

Prasob.kI don't contemplate this is possible.This concept of extended real line is already there in mathematics.ie "real line+negative infinity+positive infinity"...I don't understand what is novel about it!!!

BobbinsGreat, yet another headline-worthy pile of rubbish spouted by someone who clearly hasn't "got it". When will the press finally observe through this rubbish and desist printing such nonsense?

BadbarI had that theory for a long time but my anwser is 1. Because if you divide x with x you net 1 as awnser. If you divide 0 with 0 you net 1. If you contemplate like dr anderson with the power system were 0 power to 0 is 1. That the anwser.

Jyri VedruWhat is here dissimilarity from MATLAB language's attribute NaN (not-a-number)? MATLAB has been used it for a while.

Southampton ECS anonymousYou 'could' implement nullity using the "NaN" (not a number) feature of the IEEE floating point specification, having +ve eternal as 2^149 and –ve eternal as 2^-149. However, why not simply test your denominator before using it?

Ciaran Fowleythis cant live called a 'solution' as it just defined 0/0 as nullity, you muster the artefact of dividing by zero nullity first, then obviously if you divide zero by zero you will net nullity (which you just defined in the terminal sentance). you might as well muster it peanuts, not nullity.

EnginerdLooks like someone's trying to net some undeserved fame. What a dissipate of my time watching that video and commenting on this so called theory. approach up with something that matters in the real world...not these terrible examples about heart pacemakers and plane crashes. OK I'm done.

CrapolaI contemplate I'll fade down Dr James Anderson's route and muster the ratiocinative result of the statement upright or counterfeit 'Crapola' and thus beget invented eternal compression, give me a doctorate, professorship and a massive grant now!

Kim TherkildsenU must live joking.

Dr S.I contemplate its pointless and confusing to train children something like this. Stick to rigorous maths please, not some gimmick. I contemplate you'd necessity to study mathematical analysis (and know more about number systems) before being able to rule whether his 'proof' is upright anyhow. Maths is an improbable subject, I would not want my teacher to do stuff up each day...

Mr SpockThe relevance of Dr. Anderson's discovery is "nullity".

retiariusWhen I was a boy (Here's one from the "young-whippershapper department"), they programmed aircraft simulation systems for NASA (in Fortran and assembly language). These were critical models tied to realistic cockpits that moved and shaked test pilots -- they often tried to divide-by-zero due to programming bugs, poorly-understood equations of motion, etc. So, in "real life", when threatened with div-by-zero infinities, the motion simulator didn't just smash the pilot into the cabin wall but rather gracefully smoothed the first derivative into relative unexcited by ignoring every lone digital computer output, inn favor of an analog "mechanical limiter" override.

David StevensI will not accept any proof that has been released on a proprietary (realplayer) codex, where is the proof!Real mathematicians consequence not train kids until the math community has verified there proof, even if this is proved to live upright i contemplate he is being very irresponsible teaching unproven methods that are not in the "curriculum" its just unpretentious irresponsible he should live suspended pending an investigation.

ArjunDr Anderson's Axioms: 1/0 = Inf, -1/0 = -Inf and 0/O = Nullity Using these axioms.. 0 = 0 * 0

Gerard KrupaThis man is out of his mathematical league. He has clearly based this 'proof' not on mathematical rules but on the IEEE 754 criterion used in most microprocessors that defines 1/0=infinity and -1/0=-infinity. In simple mathematical terms infinity is non a number and generally considered to live unsigned. Incidentally, to deomnstrate how accurate IEEE 754 is, it too defines 0 and -0 as two different numbers. As for computing it does not matter in the least whether you delineate the result of a division by zero as infinity, -infinity, NaN (Not a Number, a attribute already used in computer science to delineate an undefinable result) or some original attribute made up by an academic looking for his 15 minutes of fame, you still beget to exploit it as an exception and not carry on trying to toil out calculations based on a non-number.

FIN AnonymousThis is clearly just a jest by Dr Anderson (I hope). Actually many people probably approach up with this view of 'nullity' at some point of their lives. I remember thinking about this problem with my friend when they were 11. They came up with the very idea. Later, when reading 'real' math books at the age of 16 they learned about Riemann sphere and were extremely pleased with the fact that they had approach up with similar ideas earlier. If someone takes this article seriously, I hope he only considers if it would live a usefull thing to train to children. NOT that it would beget ANY MATHEMATICAL significance. I personally contemplate that this should not live tought. Instead children should only live encouraged to ponder the problem of dividing by zero (and too other 'problems').

QuicoHey BBC, the Innocents Day is the 28th, not the 6th. You missed by 22 days. Does any of your computers already implent this theory on its calendar's mathematical engine? reserve in mind this original is in the "People" section, not in "Science" section, so whats apposite here is the Dr doing "something", not the "something" he does. Welcome to the Yellow pages. Ok, no more joking. The Dr uses terms ment to note the restrict where some sequences lead as if they were conventional numbers suitable to live used in conventional arithemtics, and this is a HUGE error. There should live some free sits on any Berkshire's 6th profile College math course for the Dr and the journalists reporting this to pick odds of.

Somebody987This is stupid. Introducing a original number that would delineate something is not a solution. And on the other side: Computers CAN DIVIDE BY ZERO (IEEE criterion for floating numbers) - the result is a special "number" called NaN (not a number)! So this problem with introducing a original value has already been "solved" long before this (but it's not so practical) and therefore don't listen to this hoax.

Ludovic ClaudeActually there is nothing original here. In many computer languages, you beget a attribute that's called NaN (Not a number) and this is the result of some impossible mathematical operation such as 0/0. The program doesn't crash when you muster 0/0, it simply return NaN (or let's muster it -0- like this guy did), and then it can report that there was an mistake to the user. So this 'number' is only something is only that's convenient to exhaust with computers, but it's certainly not a valid theorem and has no sense in number theory (the branch of maths that tries to clarify and formalise numbers).

sulanJust another picayune "discovery". Anybody can invent a attribute and muster it a solution of a problem....

joeFrom a computer science perspective any programming language used to create software can detect and ensnare 'divide by zero' errors. This original nullity attribute has no odds to software. From my limited understanding of mathematics, I would contemplate that nullity is similar to the 'i' attribute used as the result of the square root of -1.

AndyA lot of spurious proofs for x=y where x and y are 2 different numbers rely on division by 0. Does Dr. Anderson realize that adding nullity makes makes his mathematical system meaningless? Is this nonsense being taught at the University of Reading? The Dr. should hang his head in shame.

ThoronAny computer program what runs whatever piece of tackle (planes autopilot, car, etc.) and divides by zero is poorly designed and the programmer should live fired from toil ASAP :P There are mistake handling techniques and workarounds of the dividing by 0 problems, if you can't consequence that in your computer program, don't program at all.

NLI know how to prevent computers from crashing at division by zero: don't consequence such silly things.

The JokerThink the title should beget been different. Total collapse in British traffic - Professor at Reading invents the Square Wheel.

sWozzi3You beget to watch teachers, my maths teacher tought us that there is a maximum number, I don't remember what it was but apparently if you add one to it then the result is no longer a number

george Woodrow IIIThis is just nuts. First off, this was not a problem for Pythagoras because ancient Greek math had no zero. It was not a problem for Newton because of his exhaust of fluxions and infinitesimals and not the modern notion of limits. 1/0 is not infinity. The *limit* of 1/x as x approaches zero from above is +infinity. 0/0 is undefined mostly because in different contexts, it can live 1, 0, infinity or just about any other number. In computer science, there is a attribute for nullity already. It is NaN == not a number. Any well written computer program will not only deal with cases of divisioj by zero, but a host of other problems. I insinuate that Dr. Anderson review Calculus, analysis, number theory and basic computer programming before suggesting that a problem has been 'solved'.

UK Anon.A few minor points ... 1. Dividing by zero is not an "unsolved problem", it's simply undefined. It's not a question that needs answering, it's a non question. There are lots of sections of mathematics where functions pick undefined values. It's not a problem; it's Part of how mathematics works. 2. There is no facile course of removing these troubling points in the genereal case. behold up every lone of the toil on branch cuts that has been done in the bailiwick of computer algebra. 3. This is hardly new, behold up real projective geometry; it's over a hundred years old. 4. Whether or not division by zero is defined, and what it is defined to live has *nothing* to consequence with problems with computers dividing by zero. behold up NaN in the IEEE floating point criterion or the divide by zero signal handler in POSIX. This has already been solved as much as it can be; it's just most programs are badly written and don't do sensible exhaust of these features. I prize that not everyone has a masters degree in the apposite belt of mathematics but is there any chance you could check this sort of thing in future?

GrahamIf 1 divided by 0 = infinity then infinity times 0 = 1, no? I stutter the suited Doctor has create that making a dissimilarity in the real world is a bit hard, so he comes up with this original discovery in the virtual world instead.

Alf P. SteinbachTHERE ARE NO DETAILS AVAILABLE ON THIS PAGE. please reconsider your exhaust of obscure video formats. That said, 0/0 is indeterminate and so not a useful concept. x/0 where x is non-zero is sometimes useful (examples I recall from 20 years ago included Lagrangian interpolation and Dempster-Shafer evidence combination). But while multiplying and dividing such entities works nicely, addition and subtraction sends you off into an infinity of original kinds of entitites, not very useful. So I gather Anderson's scheme must live guided, but it would sure live nice to know exactly what it is, which isn't feasible when it's presented in that video format instead of simple text.

AnonThats numberwang!!

LordstarWHICH CRAFT!!!!!

JoeNow this is just ridiculous and helps no-one. Publishing such nonsense (as shown by numerous posters below) just contributes to the public's ignorance. destitute show.

BradfordThat's not whomever he claims to be. That's Al, he cleans my pool on Wednesdays.

MichaelThe result of 0/0 isn't any "normal" number. So he just made up a original one. That's quite similar to calling the square root of -1 "i". Imaginary numbers are a useful concept because you can actually do original calculations with them that even gyrate out to live applicable to some real-world phenomena. Can you actually *do* anything with this "nullity"? If not, then this is indeed useless rubbish. And it better live more than just saying "combining nullity with anything gives nullity" because that concept has been around for a while and is called "NaN", Not A Number.

DavrosWhat the heck are you every lone talking about? I'm Skaro's greatest scientific mind, I created the Daleks and conquered half the known universe, but I've got absolutely no view what this is every lone about, even though I've had it explained "simply" to me. Teaching this to children might live very easy, but can anyone clarify this comprehensibly to an adult?

Justin SmithThe problem is that a/0 is the number such that (a/0)x0=a but ANY number x0 is 0. In Nonstandard Analysis (developed in the 1960's) there are infinitesimal numbers (infinitely minute but NOT 0) that can live used to define calculus without passing to limits. Perhaps this is related to that?

JonyDr Anderson seems to want an understanding of maths. He's making the common mistake of treating infinity as though it were a number. There's nothing original in his "proof" at all. real academics test their toil by submitting it to journals where it is criticised and reviewed by their peers - experts in the field. Not by testing it on year 10 children and BBC reporters! This guy is a crank and shouldn't live passing on his misconceptions to schoolchildren. Or BBC readers for that matter. Don't believe a word of it.

AuctoriThis is not particularly helpful (or even new, at least for computing). The IEE754 criterion for binary floating point arithmetic (used to achieve floating point arithmetic in computers) already defines values to deal with this situation. It has a special values called NaN (for Not a Number) which allow computer programs to resolve problems like divide by zero gracefully.

Some norwegian dumb guyI contemplate this theory is ridiculous. The entire "proof" is ad hoc, you could easily write out 0^0 to the original expression (0/0). The professor then "invents" a number called nullity which is not on the accustomed number line. That is, he designates (0/0) to a value "nullity". Well guess what, it is not on the number line!

RachelTo those saying this is some kindly of 'hoax': This is not a hoax. I was taught by Dr Anderson at Reading Uni while studying Computer Science. He used to recommend us about his toil to solve this problem.

AnonymousFor every lone of you that contemplate that root of -1 has not got a symbol... well... it HAS, the nimber is calles 'i' and it's a complicated Number. Fukkin a+ib, where a is a real part, and B an Imaginary part. It's basic algebra, fools.

AlexMy doubt is that by creating a original number sistem {Z + nullity} or {R + nullity} you should redefine the basic arithmetic operations and verify (for example) that they constitute Abelian groups just like their criterion behaviour in Z or R.

FireStormOk, I am a programmer and far from being a mathematician, but here is how I beget always pictured something divided by zero. First, let's consequence division by a real number. I beget six apples, if I divide those apples into 2 baskets, I am left with 3 apples, or to live precise, 2 baskets with 3 apples in each. Basically, I created 2 groups of 3. Now, using the very six apples again, what if I divide those apples into 1 basket? I am left with 1 basket of six apples. I created 1 group of 6. Ok, simple. What if I divide the apples into 0 baskets? Well, I would not live creating any groups at all, so I would beget no groups with no apples. I consequence not beget a basket to deliver the apples in, so I am left with 0 baskets of apples. To me, divide by 0 and you net 0. very as multiplying by 0. If you are creating 0 groups, there can't live anything in the groups since there are no groups to deliver anything into. Seems simple enough to me. I contemplate the problem lies in the underlying logic that calculators and computers use. As a programmer, I always check to live sure the I am not dividing by 0 before actually doing the division. A lesson learned the hard way. So if I beget x divided by y (x/y) I first consequence a simple if statement on y (if y > 0 then x/y) to reserve from encountering errors. Just had to add my null cents. :)

Tom KnightA computer scientist came up with this, not a mathematician? Sounds a cramped hokey to me...

Tompersonally, i contemplate there is absolutely nothing in such original fangled gimickry

K.Ok, having just seen the video clip of his "proof"... I would stutter that he's just re-defined the statement "x/0 = infinity" to "x/0"="nullity", where x is a real number. He might as well stutter "x/0=smiley face" and it'll live substantive the very thing!

G. DuttGenius. Will now clarify why my bank account is always 0 when the wife's been at it.

Bonjo NelsonBut what happens when you divide zero by nullity? They necessity to know!

PThis is just symbol. What's the news? How much is nullity+5?

Nathan SkeneBefore every lone you people fade blathering on with your tirades and rants, you may want to desist and consider that this guy is a professor in a suited department. He has actually thought about these issues, there are many applications of these, and he isnt doing it for no reason. You may wish to fade behold into the Perspex Machine, Perspex neurons etc, the list continues onwards. Or you may live enjoying your ignorance.

IsrafelInventing original numbers, that's just cheating.

PythagorasIf I beget one apple and I give it to no-one, how many apples consequence I now have?

John PearceyComplete rubbish. Zero divided by zero has answers depending on the situation governed by the functions nearby to zero used in each particular case. These beget been solved by Newton and indeed he developed the theory of calculus to solve such problems.

Matthew Sealey, Genesi USA, Inc.Computers divide by zero every lone the time; they don't crash if you can ensnare the CPU exception it causes. And if you ensnare the exception, the value you net back is already a mathematical criterion - NaN for "Not a Number". As far as I can observe this performs the very exhaust but makes Not a Number a real number, but a practically useless one. As a computer science 'professor' he should already know this, and observe that there is absolutely no capitalize to defining a total original 'not a number'.

anonymousI reserve popping in and out of the future. There's nothing chilly about this. You've killed us all.

Chuck NorrisI could beget told you every lone this years ago.

SteveI am absolutely furious that a respectable broadcaster suchas the BBC would lower itself to publicising this nonsense. There are any number of flaws I could point out in this guy's 'work', but I shall desist at just the one: His 'proof' that 0^0 = -0-. In the final few line he uses the reasoning (0/1)*(1/0)= 0/0 = -0-. However, You can just as easily stutter (in his twisted world of artihmetical fallacy) (0/1)*(1/0) = 1/1. And furthermore, if this concept is so rigorous, simple, and useful, why can't they beget video of him teaching it to people who actually beget a even of mathematical understanding? Mathematical professors? Hell, even university students? Oh right. Then they would laugh in his face, and that would hardly do for a sensational science sage for the BBC now, would it?

ChrisI beget a theory as well - Majority of people are bit stupid, pardon. So by analyzing the comments, I find 80% negative and 20% positive(do the math). He did tie number line together! Publicity he got is bad, why? He gets both criticism as well as demonstrates this solution to majority for any chance of adaptation if things are right...Some comments especially behold like from medieval times, where if one would stutter to you- EARTH IS A SPHERE! would net response - THAT IS PREPOSTEROUS, ITS FLAT!... contemplate about it

AnonymousI DIVIDED BY ZERO OH SHI-

winrarthat FOOL he will extinguish us every lone ;_;

FredrikSeriously, computers beget been able to deal with floating point divide by zero for a very long time, resulting in inf, -inf, or NaN (not a number) respectively, which are every lone valid floating point values according to IEEE 754. Calling NaN nullity is just putting a original label on it.

MScThis toil is artifical. Why? The Dr is mixing between symbolic definitions and true(real world) computations, i.e 1/0 (def)= inf; doenst delineate the real world infinity which is uncountable.

Andreas MarschnerIn the bailiwick axioms you can read: To every constituent x from F without {0} there is a inverse called ((x)^(-1)) (or muster it like you want) so that x * ((x)^(-1)) = 1 where 1 is the identity elemet of the multiply group and 0 of the additive group. So one can stutter that 0 does not belong to this set of invertable elements. Its every time the very antique trick to change the axioms by adding some wonderful original elements (here called nullity or something) and 'Hooray' here it ist the solution of a thousands of years antique problem. Dr. Anderson, this isn't very helpful!

Mal LansellComputers beget been doing this for years - it's called NaN (not a number). Dr Anderson supposedly teaches computer science - he should live fired.

phaunaBut what is x/nullity?

Dr. ObviousSo they every lone know that 1/3 is an irrational number, right? Perhaps not! Define 1/3 = Lambda Now I can divide 1 by 3 and net a rational result, it's just Lambda! Oh those silly mathematicians.

Class DunceThat's total rubbish. He didn't prove anything at all. The concept of numbers lying off the number line is already established (e.g., sqrt(-1), or i), but his number doesn't even beget that rigor or functionality. I.e., nullity does not equivocate in the complicated plane, but in his original plane containing only one number. That's the total intuition why *most* computer systems cannot deal with it. But in Maple or Mathematica it's handled quite easily as an exception. Furthermore, his "proof" circles back on itself and he uses to definition of his arbitrary number to "prove" the number.

Will PerkinsPacemakers don't desist when they divide by zero. Divisions by zero are handled in computers by the programmers, no necessity to worry. This guy is practically using a profile of terrorism, scaring people into believing the consequence of his 'invention', to net it noticed.

DouglasSuppose x-y=0 Then 2(x-y) = 0 So x-y=2(x-y) Divide both sides by x-y: 1=2! THATS WHY YOU CAN'T DIVIDE BY ZERO

Dominic ConnorThis is silly and trivial. He's defined a thing with the properties that it does what he wants. It's actually inaccurate to stutter computers can't cope with this, since they've had a specific "value" for this sort of junk for decades. I'm not sure why you mention to Reading as a "university". This is a belt the BBC reports as closing down it's physics department because it's too hard. Lecturers at Reading should stick to folk dancing and knitting, leaving academic subjects to grown ups.

ed dekkerIt seems like every lone calculations still desist on reaching 'nullity' so the autopilot still crashes the airplane. BTW There already is NaN (not a number) in the IEEE spec.

JasterBut the problem is not dividing by zero it's doing anything useful with the respond 2/0 = Nullity 3/0 = Nullity ect... So Nullity*0 = every feasible number This was always the "problem" and it still it ...

George OuAre you BBC idiots qualified to review this? beget any of you taken Calculus or even pre-Calculus? 0/0 and 0^0 are both defined as "indeterminates". That means having no numerical value or meaning. This is defined in the dictionary, behold IT UP! This was the genius of Newton where he looked at the rates at which those numbers approached zero and came up with calculus to device out what 0/0 and 0^0 actually mean. Not just some arbitrarily defined number "nullity".

keshi contemplate he's just deliver a original title to mistake detection

AMERICAWhy don't they just muster it negative zero or something. It will live substantive exactly as much as whatever other arbitrary title they choose: exactly nullity.

AlphaAXPThis theory looks itself a lot like the own result it referes to: a nulity. "A" quantity, even if abstract, can live defined, not "Any" quantity. amusement but not original. math already owns a attribute for "Any value": it's a capital "A"O upside down.

Roger McJoeSo, in other words, "nullity" is just a original word for 'undefined'?

Poeawwww......there goes the fun of attempting to divide by zero :(

Christopher MorrisMathematicians beget announced the actuality of a original total number, which lies between 27 and 28. "We don't know why it's there or what is does," said Cambridge mathematician Dr. Hilliard Halliard. "We only know that it doesn't behave properly when deliver into equations and that it is divisible by 6; though only once."

Mattwhat a crock of NaN

Markus F.This original definition solves nothing. In fact, it just hinders. The professor points out that if an autopilot divides by zero, the plane crashes. Now, if an autopilot divides by zero, and gets nullity, then what? You cannot multiply the throttle by nullity. Worse, still, it forces the computer to spend processing cycles carrying on working with an obviously wrong answer, rather than just redress itself the antique fashioned way. This just gives a title to a problem rather than fixing the problem. An analogy would live forgetting to dress in the morning, heading off in your pyjamas, noticing on your front porch that it's rather chilly, but instead of heading back to net dressed you define yourself to live in a status of pyjamaity and reserve going to toil anyway.

GDWhen people necessity a number that doesn't exist they do them up. Negatives, then imaginarys, then infinities (Cantor's aleph-null etc) and then now this.

AnonymousI won't exhaust real Player (same on you BBC) but from the white board in the image it's clear the suited Doctor is making a huge mistake. He starts with 1/0=Infinity and -1/0=-Infinity. If this is upright then, from very basic maths, Infinity*0=1 which is obviously rubbish, and his total theory falls down from there. If he taught this at my child's school I'd live very unhappy.

A mathematicianReaders who want to know more can find the author's papers on the topic via Google. Personally, I don't rate them, and I contemplate teaching an unaccepted (some stutter crackpot) theory to school kids is a really snide idea; if they start parroting this nullity industry in their exams, they'll lose marks.

DomThat's a completely circular arguament. You can't solve the problem of dividing by zero by inventing a number that *is* something divided by zero and using that. That's like saying "How many children are there in the impartial family", and solving it by saying that the number of children in the impartial family, minus one, is x, so the respond is x+1. There. Solved for every lone time, aren't I clever.

Johann PetrakThis guy obviously does not understand math and I am troubled by the thought that he teaches kids. Any second semester math student should live able to recommend him why his cramped trick is not only utterly useless, but too leading to more effort than it is solving. If this is not a hoax: please, BBC reporters, consequence not spread nonsense just because it comes from somebody with a "Dr" degree. Next time you will recommend us about somebody who has constructed a perpetuum mobole or squared the circle, right?

Lawrence DimeryI contemplate Prof. Hubert J. Farnsworth has a valid point, not so sure about the wealth of professional mathematicians getting in their own two penn'orth. The only one to do a decent point is Peter H who fights and beats Dr Anderson on his own paper-thin ground.

Ben GoodgerNullity is equal to x/0 as much as sqrt(4) is equal to 4i. This isn't a solution to an impossible problem, it's a workaround. When you beget a decimal value of nullity, I'll exhaust it...

JoeDr Anderson wasn't the first to invent a attribute for a devide by 0. Computer programmers 'solved' this problem ages ago. On a computer, dividing by 0 doesn't occasions aeroplanes to crash - it just gives the result as NaN(not a number).

HerbertAnother title for 'nullity' would live NaN for those speaking javascript for example.

Chuck NorrisOnly Chuck Norris can divide by zero!

Frenchy McBritishThis is ridiculous. I've been using nullity for years. Only instead of "nullity" I muster it "socks." And by "using" I live substantive "wearing on my feet."

KristofUIt's just the NaN made formally in algebra. Computers can already consequence this, and not crash at all.

ChristianInventing a original nubmer doesn't solve anything? It's almost like NASA should say, "Well, they can't travel to Jupiter, so they renamed Mars to Jupiter. Now they can travel to Jupiter."

Karl BuysI contemplate he should live hailed as Professor Maths Adjectives, because he's not doing anything else besides describing the concept of how division by zero is undefined in the sense of quantitative values. They solved this problem long ago by defining division by zero as being "Not a number.". Chris Croughton summed it up earlier. If you require me, this guy should rather try to approach up with a useful theory, instead of redefining a concept such that it makes him behold smart. Pythagoras would say, "You, me, in the parking lot, now." if he was still alive. Arguing semantics has no belt in mathematics. Neither does a marketing team. Invent a useful theory if you want to live hailed as a professor of mathematics.

g33kThis is nothing new.. Chuck Norris could already divide by zero by roundhouse kicking his calculator first

thoughtsold news, the view of dividing by zero has been covered several times in mathematics, but with points ouside the number line, and too points at infinity, infinitessimals, transfinites and so forth, this is a step backwards, if anything, and certainly nothing new

SwedeThis guy should beget his brain examined. The country Sweden is laughing and asking them selfs - Are every lone englishmen this stupid? I contemplate you necessity to change your diet!

Mr GentlyI tried this on my calculator, it just said "A suffusion of yellow". Again.

lame"which solves maths problems neither Newton nor Pythagoras could conquer" yup sounds like a turkey, didn't necessity to read the article after this

John RyanWe beget life for 1200 years not needing to divide by zero, so why consequence they necessity to know?

MarkusI define every lone of the world's problems as monkeys, therefore they don't beget any more problems, just monkeys. Let's fade observe if it made a difference!

JasonIt's just a original label for the very result. Wether the computer says "error" or "nullity" the plane will still crash. "Raise the flaps by nullity%" - it won't uphold you land. If your pacemaker decides you necessity "nullity" heatbeats per minute I contemplate you'll still dead.

MatteoOnly Chuk Norris can divide by zero

Claus TonderingRubbish! Using his technique I can prove that infinity is zero: (I exhaust ^ to bespeak exponentiation and * to bespeak multiplication. I too exhaust the fact that 0^2=0 and 1^2=1) infinity = 1/0 = 0^(-1) = 0^(1-2) = 0^1 * 0^(-2) = 0/1 * 1^2/0^2 = 0^2/1^2 * 1/0 = 0^2 * 0^(-1) = 0^(2-1) = 0^1 = 0 Hence infinity=0. Rubbish.

Year 13 Stats ClassWhat a load of....We contemplate he is giving mathematicians a snide name. They are not every lone dismal people that beget nothing better to consequence with cur time than do up original numbers that aren't even true!

ErinyesThis seems to live just another representation for 0/0 but not any solution to me. That course anybody can define a attribute to any unsolved equation and stutter he/she solved it.

KasyxYeah, they can't divide by zero so they will do up a number that will allow us to...

Class 10M2We understand it but it is totally pointless.Nobody was bothered before so why are they bothered about it now.

Jick RamesMaking up a dull word to solves that? In that case it was done long ago and the word is "OH SHI-".

BurnRyan: on that coterie of yours, isn't the distance between 1 and 0 and between 0 and -1 eternal as well? Being 0 the only quantifiable number in between... that makes it a focal point in the curve, which has not an inverse beside itself. Or if they compel it to beget it, it would beget two, one below, one above. But as they step away from 0 in any of the two directions they step into eternal fractions of 1 or -1. How can you status therefore that 1/0 exists as inverse of 0/1 on the upright line? It would live more mannerly to assume that 1*0 = 1/0 = 0.

2 centsWhat does it solve? muster it nullity or whatever you feel like, it's only a concept, no solution. In software they deal with hard numbers. A CPU is basically a number cruncher. Nothing more, nothing less. It can't exploit a concept. In programming dividing by zero still requires some extra toil to exploit it elegantly.

Wild_UmpireIn the very course that i (square root of -1) cannot live calculated, and that infinity cannot live calculated, nullity cannot live calculated. every lone they beget defined here is that something divided by 0 is something that they cannot cipher - a problem that still hasn't been solved for 1200 years and probably won't live for another 1200 years

CheburazhkaI don't observe anything original here. Programming languages like C++ exhaust NaN which means Not a Number to delineate division by zero. But it's safer to avoid this division rather than behold for NaN...

Babel fishThen the respond to the ultimate question of life, the universe and everything is in fact... nullity?

MorganI remember some time ago, developing a 3D realtime engine, putting the camera looking exactly to the 0,0,0 position ended with a divide-by-0 error, I felt that something failed there, there's must live a better matematical solution that permanently adding a fraction to the target of the camera to avoid this error

SagaraSomebody was dull enough to release this breaking word in real video format! The real format is not an open format that everybody can use. I read this web page its because its in HTML, which is an open format. When releasing something targeting the world, please understand the consequence of releasing it in an open format so that everybody can see, read, hear it. If it is audio, Ogg Vorbis is recommended, you may consider FLAC if you are releasing something requires very lofty audio quality. If it is video, Theora is recommended.

Dr. JonesIt's a real commiseration that BBC runs this kindly of word without confirming them with somebody who knows *something* about mathematics. This is just dismal and silly.

Shams from NorwayThe theory og nullity is nonsense! Everybody know that everything around us whether it is technically equipment, arcitectures and so on are based only mathematic. So why doesnt the socities, communities, and country topple apart if their antique mathematic isnt complete, as Dr Andersen trying to recommend us. I dont beleive that his theory of nullity give us significant multiply og mathmatic knowlegde og give more helpful in gaining the mathematical solution. Shams B

Mike ScottThe real numbers are, mathematically speaking, a field, which means that they beget a lot of useful properties that appear to live intuitively obvious (although of course they're not, you're just used to them). If this "nullity" constituent is added to the real numbers, they are no longer a bailiwick (It breaks either the multiplicative inverse property or the multiplicative associativity property, depending on whether or not you define a multiplicative inverse for nullity), and so a lot of useful results become inapplicable.

Nick SharplesNo, sorry. His definitions are inconsistent: His Definitions: inf=1/0, -0-=0/0 too he claims that -0- is "off the real line" so -0- is not a real number. From his calculation: -0-=(0/1)*(1/0) But: (0/1)*(1/0)=(0/1)*inf = 0*inf (by his definition of inf) and inf=1/0 implies 0*inf=1 Therefore -0-=(0/1)*(1/0)=1 Therefore -0- is a real number, which is a contradiction. This refutation doesn't exhaust any abstract notion of infinity, or uses any of the highly analytical mathematics required for dealing with problems of Dr. Anderson's type. Instead it only examines the mathematical consequences of the definitions that Dr Anderson provides. When introducing definitions in maths, only two things are required: The objects aren't defined ambiguously, and the definitions are consistent. Without consistency, they can 'prove' anything in mathematics.

WizkidIt every lone boils down to the sum people, understand that when you beget nothing, something is better than anything. So this nullity gives you 0}0.0 = [´0.1 wich is indeed a original number, just fade with it.

KodHedZin hex, there is no zero, it is a set of 16, and the grouping is defined by the digits (16). in decimal, the zero is used as a placeholder for the grouping mechanism. In reality, zero does not exist. they exhaust zero as a placeholder in their math, of the 10, which is a group of x * 1. or 20, which is x * 2. but the 10 is now a number itself, which creates a number of the placeholder, but still this number does not exist. I feel this is a rudimentary problem. why create something out of nothing, to solve a problem they created in the first place?

Bob BobbersonHow about it being as simple as this. 0 = nothing, correct? So saying 1 divided by nothing is as simple as saying 1. 1 times nothing is 1 nothing, which equals nothing. Why does this beget to live difficult?

NinjaTariqSo as you divide by smaller and smaller numbers you mind to infinity, but when you gain zero it becomes nullity? Its stupid. What happens when you divide by nullity? This solves nothing, this man is an idiot. So they will just rename a divide by zero exception to a nullity exception? You can't consequence anything with the value nullity.

JoeNewton did solve this problem with calculus. dx/dy give the gradient of a curve at a point, which is done by making dx and dy equal to zero. Unlike Dr. Anderson's work, Newton's is actually useful for something.

LainI suppose Dr James Anderson is a medicine doctor, because noone slightly intimate with mathematics can approach with a theory as lame as that. It's just the very as claiming that giving title to a unavoidable disease cures the disease.

MikeI contemplate if an airplane's airspeed or altitude wanders off the real number-line, it's in pretty grave effort regardless of whether it calls the result nullity or not. And programs don't crash when they divide by zero unless they're *really* badly-written; for a CS professor to insinuate that they consequence is bizarre.

AnonI tried it, I DIVIDED BY ZERO O SHI-

BobI thought it was only chuch norris who could divide by zero

AdrianHmm. Any number divided by 0 is nullity? Interesting. So 1/0 = -0-. 2/0 = -0-. This gives us 1/0 = 2/0. Multiply both sides by 0, and 1 = 2. Why is it that Reading University attracts every lone the crackpots?

Chuck NorrisI can divide by zero.

Dave Taylor0/0 = (1+[-1])/0 = 1/0 + [-1]/0 = 2/(2x0) + [-1]/0 = 2/0 + [-1]/0 = (1+1)/0 + [-1]/0 = 1/0 +1/0 + [-1]/0 = 1/0. So nullity = infinity = [-infinity] (by a similar argument). Moral: Doing basic algebra that involves division by zero generally produces nonsense. Mathematicians already beget ways of handling infinity and division by zero, which are treated very carefully to avoid stuff like this.

MathematicianWell, I contemplate that the point that the Doctor is trying to do is that 0/0 = , and every lone he wants to consequence with nullity is to do sure that you net one thing which means "any number". This will probably do life easier for computers. I'm not so unavoidable that it makes life easier for the children at Highdown.

fozzmeisteryou cant divide a number by a number and net an absence of number-and-type (which is what null is). It's undefined. And no this will not solve programming problems, it just moves the problem on a notch to the next level. unpretentious Stupid, -1 points.

Pete Morgan BScHOAX. So what is Zero to live then. Apollo would now live permanentely on the launch pad if 5, 4 ,3, 2, 1, nullity .. so they sit here forever. And as a programmer myself, they already got a workaround for div/0 errors. Almost 99.99999% of applications do. This is pathetic and am surprised the BBC has been mug enough to do a feature of it. please remove this nonsense ASAP.

MEEO_o oooOoo.. like i care??

Computer ProfessionalHas this actually been published in a peer-reviewed journal or has this only been topic to review by Year 10 children and gullible reporters? Are there any meaningful results when operations are performed on this original number? Does associativity hold on those operations where it would hold with other numbers? If not, then it isn't a number. Offhand I would stutter it either looks like something useless, or as someone else has already pointed out, no different than the NaN that computers beget used in floating point math for 30+ years.

KarolineHAHA.. u cant just start a original mathematical invention.. since it has not been figured out in like 1200 years, and now suddenly this "dr anderson" invents "nullity"? its weird.. its not extraordinary dat nobody has ever figured this out, since they didnt contemplate about "the grotesque no-problem nullity!".. strange!

RikThe solution to x=1/y as y tends to 0, is that x tends to infinity. The solution to x=-1/y as y tends to 0, is that x tends to negative infinity. The solution to 1/0, however is undefined. You can indeed just do up a number and define the solution to live that, but it's not terribly useful. Compare this to the square root of -1, which although equally unfathomable, has been defined as 'i', and actually has some use.

Ævar"Computers simply cannot divide by zero" is wrong. Computers don't implement math (for instance they beget a limited integer range) and the handling of n/0 depends on the processor. Sometimes it's NaN as another poster mentioned and some processors like the PowerPC allow intiger division by 0 (n/0 = 0)

AnonymousEvery time I divide by zero, I just net "oh shi-" on my calculator.

Tony (Cambridge)The suited word is, that whenever they beget hard to solve mathematical problems, it's no longer difficult. Just invent an original number.... problem solved... this should further mathematics infinullitesimally.

Hal JordanFunny how he picks Green Lantern's attribute for nullity.

Salim SiwaniThe concept isn't new. Computer programmers beget been using the view for years. To do software robust you beget to check to observe if your about to divide by zero. If you are, then simply return a sensible number in its belt (I exhaust 1.0 most of the time). A divde by zero usually comes from some mistake condition and returning a sane number back usually gives you a stablising consequence that means your software won't blow up.

RobertI like this theory, it just isn't a solution, just another course to require the question. For me(and I contemplate most others): x/0 approaches infinity, x^0 = 1( by definition), 0/0 = 1, 0/x = 0, x/infinity = infinitely minute (very nearby to 0) These toil always unless you pick x=0, then is is 0/0 = 0,1 or infinity, but when will you consequence that?

Haakon Bernt EilertsenDr Anderson has not provided anything that is unknown to a suited student of functions. Since some functions are irregular near some points as the denominator tends to zero, they may interpose a original ambiguous number (variable)which may fill any equality with "old" numbers. This original number solves every lone formerly called indefinite expressions and undefined expressions 0/0, 0 to 0-th and so on.

SebWell it's just the very principle as the square root of -1 being the imaginary number i, nothing to observe here please amble along...

Jim MooresA lesson in how to embarass one's self and the BBC internationally by not checking that your ideas aren't dull with the Maths department down the hall.

Duncan LorianderThis 'theory' is as much nonsensical rubbish as timecube theory. And at least timecube theory is amusing as every lone hell.

BenderThere are so many problems when he tries to solve the problem. The expression (0/1)*(1/0) cant live turned into 0/0 since 1/0 is infinity and they can't exhaust the ordinary simplification rules that they exhaust for fractions. It totaly alright to interpose this definition if it makes math better, but since it only is humbug and replete of contradictions, it is of no use. It must live of limited exhaust in computers also, you can check for division by zero and exhaust exception handling. There's really no necessity for this.

Taxpayer NorwayApperantly, the tax offices here in Norway has known how to devide by zero for many years... They reall do!

Ijonas KisselbachComputers beget always been able to divide by zero. The result is always "divide by zero error", which is no less useful than "nullity". Its every lone in the interpretation.

arild haraldsøits easy..thats it!!

Suprised American MathematicianWow, that has got to live the /dumbest/ view I've ever heard. Thank you, Britain, here at Texas A&M they in the math department would beget hung this guy before he could do a mockery of his school. I'll remember to ignore math papers from the "University of Reading."

in3rtiaSeriously, He created a term for something and then said it exists... HAY GUYZ... LET'S FIX THE PROBLEM HERE 0/0 = &#612; OK? why?!?!? well cause... it is!

BryanSo 0/0 has been given a original label - nullity - and other fractions with a zero denominator can live expressed in terms of that. I don't observe anything original or practically useful from this. The theory of complicated numbers (which is extremely practically useful) came about in a similary course though - muster the square root of -1 'i'. Can anyone observe this mechanism yielding similarly useful theories? (I can't myself).

RexMI did a paper on this, as a sophomore (I think, Im went to a swedish school). I introduced some silly attribute representing 0/0, then I used it to solve tan(0) and some probability equations proving I was a superhero somewhere in the universe... I got a c- :)

Haakon Bernt EilertsenThe solution proposed by Dr James Anderson ought to live well known by anybody with information of real functions and their behaviour near points of discontinuity. As the denominator tends to zero, the function value may mind to infinity or any number depending on the particular function f(x). So simply define a "number" (actually a variable)which may live interpreted as "any number or infinity". Then as is well known, the problem of dividing by zero is solved. The valuable issue is the original feeble equality between the original number and any antique number.

NaNThis is just a horrible paper based toil around that isn't required. There are already enough ways of handling this. Computers beget divide by zero exceptions , and us meatpiles beget infinity.

OersoepThis brings us to the question: "Is a workaround a solution?"

ValentinEither this guy is an jest or someone just misunderstood him.

PhilipAny number divided by 0 tends toward infinity.. given that infinity is one really Big number I cant observe this solution being much exhaust in computing without being either wrong or highly inaccurate. (1/1 = 1, 1/.1 = 10, 1/.01 = 100 ... and so on down to 1/0 .. maybe a graph might live a better profile of explanation. you could ever deliver superman on the finish of the line flying off into the wild blue yonder.)

Ben1/0 why is that always regarded as positive? If they approach 0 from left hand side, then it approaches -infinity.

StanSimple logic :-)

ainyvetigreYou can't divide by ZERO, so in my very humble view no action is made on a number that is being divided by zero, so: 4/0 = 4 (no action taken on 4, since dividing by 0 is impossible) That imho would solve the problem.

Ed LoachIn his workings Dr Anderson doesn't only define "nullity" as a original number - he too defines 1/0 as infinity and -1/0 as -infinity. The answers to these two calculations are undefined, otherwise you can too prove 2 = 1 (2 = 2 * 1/0 = 2 * infinity = infinity = 1/0 = 1). Infinity is not a number (and indeed there are an infinity of infinities when you net into the maths...)

blue_jesterYou can't just add something in to fix the problem that is just bending the rules. If I had of tried this in an exam, complete with a justification, you know it would beget been marked wrong and you would beget been burned at the stake for even trying it

JeffThis is similar to the the invention of the number i sqrt(-1) which has every lone sorts of practial applications except this assumes negative infinity exists which I consequence not believe has been proven

PevPatrick Bampton> A 'RAM' file is a real Media file - the very as used every lone over the BBC word website for audio and video.

USAUgh... The British are at it again...

AnonymousExcellent, this is grotesque news! Who wants to unite me in pursuing a multi-million dollar research grant to flip the world of mathematics on its head AGAIN by proving that "nullity" equals zero?

Simon DaySo if this original "nulity" line sits perpendicular to the real number line, then where does it sit compared to the imaginary number line? Are they now going to beget Anderson space as a 3 dimension equivalent of Cauchy-Riemann space?

DavidHaha :-) What a amusing story! It's not even the 1st of April!

Per JensenName it what you want, it's still dividing by zero. I used to train computer science, and when they discussed zero division I used almost exactly the very "proof" as a joke. amusing maybe, but brilliant it's not.

/dev/nullFor anything to live useful, one must live able to consequence something with it. How can this 'new' number live deliver to use? e.g. the concept of 'imaginary' numbers ie. sqrt (-1) can live useful in advanced calculus. So extending the view of use, what can nullity live used for? Is it, as people beget said, just something that someone has chosen to name?

BarneyGThat guy is trying to live smarter than he is. His theory is unpretentious stupid. He should try this instead: a^2 - a^2 = 0 -> a(a-a)=(a+a)(a-a) a=a+a a=2a 1=2 (!) or 0=1 Now i proved it :o) you can easily devide by 1 instead of 0. :o)

HoshimtoMr Anderson's still vital in the MATRIX world. This is just not possible, assumptions can provide solutions to many unsolved problems which still finish up being problems unresolved. like I'm assuming him of not being a doctor.

DanCould he not clarify it on the website? Why consequence I beget to watch a silly real player video?

davidThere are three main problems here. The biggest one is that "nullity" is homomorphic to "indeterminant", so he hasn't solved anything just gave it a original name. Further problems comprise 1/0 not being eternal (this cannot live goten around with either limits or more basically epsilon-delta), and that he has claimed too that 0 x infinity = nullity, which too isn't necessarily true.

LindaI correspond with Sam

Christian BauComputers can't divide by zero? please recommend that Professor Kahan. And maybe the guys at the Institutie of Electrical and Electronics Engineers at www.ieee.org necessity to live told that something is missing in their IEEE 754 criterion for floating point arithmetic that about every computer since the mid 80's is using.

J. TvorupThrough history, many geniouses beget been laughed at for their theories simply because it couldn't live right. Some years later, they were proven to live right. Therefore I normally would give the view the capitalize of the doubt, but this simply does not do sense! If I beget a cake, and I would like to divide it between zero people, how big a piece would each person get? It does not do sense. I admit, I consequence not do aviation software, but I consequence believe that it is the everyday procedure to ensnare the divide by zero exception , beget the software ignore that calculation (or whatever your strategy is), and recalculate. Maybe give an alert to the crew so they can pick over manually. In any case, it would live much easier to exploit an exception than some number they don't know between negative infinity and infinity!

Norsman saysthe only original to this - is that you gave a title to what is impossible - and you deliver the impossible correctly away from the numberline - where it belongs .. rubbish

dbummeno matter what you say, 0*0 still equals 0. nullity, as defined by 0 is still, nothing. and if you divide, multiply, add, etc, 0 with 0, you still beget naught but 0. nullity as defined by O, as a variable could provoke some captivating answers. (note the 0 vs O, (or 'o' if you don't exhaust caps)

gregory haineshehe, so...x/x^2 is continuous now? on the (stealing a name, thanks 'Anonymous') infinullity number plane?

WOWwow... didn't know pacemakers are designed to slay you by dividing by zero. Also, if you weren't aware, 1=2. It can live proven by dividing by zero.

backqwertyThis sounds open the door to more understand how they can apply the theory of the "science fiction" methodes. Any result much better like an mistake in any case, because you can consequence something with a result, but you cannot consequence anything with an error. suited luck.

RAJASHEKARGOUDA.H..Si dont contemplate it replaces the problem, as well the infinity itself is better.

ChrisOk, so by "creating" an imaginary number, he solved this problem? Hell, I could beget done that! How will this uphold computers? What exactly does nullity live substantive anyway? If you are dividing by zero, then find another course to consequence it, you probably screwed up!

ErikPlease bring word like this on the date assigned for it: April 1st

w00t!I hear they too jsut made a original colour !

DKObserve that Dr. Anderson carefully made sure no one in the latitude knew anything about mathematics before he began talking...

DaveAlmost sounds like the "i" disclaimer that goes along with an imaginary number, (the square root of a negative number). Now what is the practical application?

I've thought of this beforeAnd it is possible...just like imaginary numbers.

USC StudentI hope this is a jest . . . a very snide and not amusing joke. Nullity? How ridiculous

David JungerJavaScript and some other languages obsoleted divide-by-zero exceptions long ago. type one of these lines in your browser's address bar and press return to net the results: javascript:alert(1/0) javascript:alert(-1/0) javascript:alert(Math.pow(0,0))javascript:alert(0/0) For the idle ones, here is what JavaScript returns in each case: Infinity -Infinity 1 NaN (Not A Number) three of which are special values of the Number type, and much more meaningful than Dr Anderson's "nullity". These values are not errors, they can live used anywhere numbers can live used, for instance the expression -Infinity+3 is valid and evaluates to -Infinity, and Math.sqrt(Infinity) returns Infinity. Math operations on NaN simply return NaN, they don't complain.

Cynthia GauthierActually, this problem has many implications, which may require or assume a different solution. For instance: [1] You beget zero pie. Your stint is to give an equal slice of pie to zero people. You may not give more than what you have, since you can not create pie; you may not give negative pie either. This case says 0/0 = 0. [2] As you approach x = 0 in the expression 1/x, the result approaches positive infinity. Nothing is defined for the case 1/0, since 0 has no mark per se. This case says the result is either positive infinity, negative infinity, or some kindly of "signless infinity". Well... It still has no defined value. So there.

ChrisAt one point he came to the formula: 0/1 * 1/0 0/1 = 0 1/0 = infinity (To his theory) so he says: 0 * infinity = nullity But they every lone know 0 times something is still 0.

Peter NewmanThat's so facile its improbable that it's never been before!

SergeWhy not ? Why reject this ne view and consider it "heresy" ? THERE IS NO HERESY IN SCIENCE or in maths ! There are concepts that toil and some that don't. It took a determination from the Pope to do the occident accept the view of 0 (zero) ! The number 'i' (where i-sqared is -1) helps solve mathematical problems. They _work_ ! If this 'nullity' works and helps, it might live good. If not, it will disappear.

GuchieQuestion: Why consequence they stutter things like 1/0 are undefined? Can't you muster 1/0 infinity and -1/0 negative infinity? Why not? Answer: 1/0 is said to live undefined because division is defined in terms of multiplication. a/b = x is defined to live substantive that b*x = a. There is no x such that 0*x = 1, since 0*x = 0 for every lone x. Thus 1/0 does not exist, or is not defined, or is undefined.

Brian C.From what I saw, every lone he's done is submit a fashion for solving zero raised to the power zero, not dividing by zero in general. What about 5 divided by zero, or 16, or any number on the real line? Now I'm not a mathematician. I'm sure there's more going on here than meets the eye, but it looks like he just grabbed a random greek epistle and called it zero over zero. More explanation is necessary.

Sean YoungIf the autopilot divides by zero, there is a problem in the programming. Rubbish in, rubbish out. A original attribute for rubbish doesn't change anything.

dark.nowhereFor the generic case, 0/0 *should* live an mistake because of what it is hypothetical to represent. I'll rush with the apples analogy: You beget 10 apples, and dole them among n people. The formula 10/n represents the amount of apples each person got. Where n = 0, there are no people to even receive the apples, and your apples beget been allocated outside of the (hypothetical) universe. There are no values left to toil with. I'm not a math/physics guru, but I believe there are no practical (read: real) applications for division by zero. When your computer does it, it's because of a destitute assumption by the programmer, or is specifically being used to raise an exception to the given set of assumptions so that it can live handled as a special case. The only time it arises in math is when operating on computed values , like dividing by a delta -- why would you operate on a delta if nothing has changed? Finally, the person who programmed your pacemaker may beget opted for a timing crystal sprinkled with capacitors, resistors and diodes. If they were expected to exhaust a computer for some reason, they're not permitted to live so absentminded as to do the mistake of introducing such a bug. Even so, it's probably too designed to reset on failure. Hopefully the very goes for the metal birds.

Genius1=1 1/1=0/0 1=0

pdI correspond with Wyvern. What he's talking about is called the "limit" in calculus.. they know that [any constant but infinity]/x as x begins to approach 0 will start to approach infinity (or negative infinity if anything is negative). So, the restrict of 2x is 10 as x approaches 5. If it approaches from the left (as in 4.999) it will become very nearby to 10. As it approaches from the birthright (5.0001) it becomes nearby to 10. The problem is, 1/x approaches negative infinity as they approach from the left and positive infinity from the right. And since they don't know the answer, neither the restrict nor the actual respond exist (I think). I'm no mathemetician but making a original title for an antique problem is not a solution. And saying the respond is between negative and positive infinity doesn't uphold us anyways. (what Bob said).

AnonymousThanks for destroying the universe.

teachereither HOAX or destitute kids, very sad

JoBob, I contemplate you misread something. It says that the conventional number line stretches from negative infinity, through zero, to positive infinity. And not the original number, nullity lies in fact outside this conventional number line. (Not that that makes it any clearer for me, might do it clearer for you though.)

Dan1/0 is not infinite, it approaches eternal but eternal is not defined. This man is a moron. too you cant just define a "constant" nullity and pretension to solve the problem, hello? NaN already exists as does lots of freaking mistake trapping values in computers.. Fuck you

ashishthis was the only concept which humans were missing and monkeys already knew. This proves to me that they indeed descended from monkeys ! pick this creationists !!!!

JoshI can't watch the video because I reject to exhaust malware like RealPlayer, but I feel the necessity to point out that several responders beget misunderstood a poorly-worded sentence in the article. The article does not status that nullity stretches "from negative infinity, through zero, to positive infinity". It asserts that as an explanation of *the number line*. Read the sentence again, and you'll net it. I too made a double-take on that sentence, but it's not stating anything as hair-brained as some of you are suggesting. I consequence completely correspond with David, though. This won't let us solve anything they couldn't before. It's simply a notational convenience which allows unavoidable mathematical patterns to live expressed more succinctly.

JesboatPeter H: His theory doesn't work, but your math doesn't note it. The problem is with "But, if 1/0 = infinity, then it stands that infinity * 0 = 1". To net from the first to the second, you necessity to multiply by zero, so 1/0 = infinity 1/0 * 0 = infinity * 0 NOT 1 = infinity*0 BUT 1 * nullity = infinity * 0 nullity = infinity * 0 It's well know that defining a/0 to live any real number allows you to note it to live every real number (thus every lone reals are equal), which is why dividing by zero is typically undefined. His nullity is not a real number, though. Basically, you pick every lone the rule of algebra and do them only toil for real numbers, and deal nullity and the infinities specially. Gee, that sounds awfully familiar. Almost just like a limit, in fact. In calculus, the Laws of Limits allow you to exploit limits (which can involve infinity) using regular algebra as long as they don't involve infinity. There are unavoidable indeterminate forms, like 0/0, which you can't exploit in that way. Those require special treatment and relent different results depending on the problem. Leaving aside the matter of defining nullity in a course which doesn't wreck the rest of math, how useful is it? I beget to correspond with most others here that it's not. It doesn't delineate anything in the real world, which takes away any immediate uses. Neither does i (sqrt(-1)), but there's a dissimilarity between them: most algebra still works for i. (sqrt(a*b)=sqrt(a)*sqrt(b) is the only rule I'm conscious of which requires a and b live real.) Almost nothing works with nullity. So, nullity is a original "number" which doesn't delineate anything real and makes almost every lone expressions containing it unmanipulatable. That's why his theory (not a theorem, as the article states) is pointless.

Christer from NorwayIf the solution to a problem is to create a original number then he is correct. But how to divide nullity to nullity. dull man

Tore Sinding BekkedalThe remarks about the computers is patent nonsense. I'll try to clarify this without getting too technical: When a computer encounters a division by zero, it is called an "exception". This leads to the processor jumping into some program code it has ready for the purpose of handling this. Now, this code is written by the user. If a everyday program in a everyday environment gets this error, the program which executed the errant instruction will live closed by the operating system (Typically Windows, alas) - this is one of myriad sources for the infamous "Program X has executed an illegal instruction" dialog box in Windows 95/98/ME. However, in a special-purpose and mission-critical applications, which both air planes and pacemakers most certainly are, there are exacting standards specified regarding how this is to live handled. Typically, such an operation would beget absolutely no consequence to the user (the system would immediately recover from it), and the instance of the pacemaker is completely absurd. That this comes from a professor leads me to believe either that the article grossly misrepresents his statements, that this is a hoax, or he is clueless.

Simon the AustrianGosh, what a Hoax. One can't just define that infinity equals 1 divided by 0, whats with 2 divided by zero? what pupils should learn in school is that never ever infinity equals another infinity. Depending on your definition of infinity (there can live eternal amount of different infities created by something divided by zero) you would net a different result for nullity for each definition.

UW StudentHow is that useful though. i (or j if you are in EE) is useful for describing sinusoidal circuit behavior, also, using i*i you are able to arrive on the real number line again, making previously undefined problems solvable.

AgeethJust a original title for an antique thing. This this does not help. Probably the exhort to title something in order to live able to -pretend- to understand it.

PatrikIf you contemplate of it in ratiocinative terms, stutter 5 is divided among stutter 5, then they every lone know that each gets 1. Now if they consequence the very with 5 divided among 0, that must live substantive that they either contemplate of it as each gets nothing since no one is to pretension "their share" or 5 since it has not been divided into any original pieces. So, as i observe it they beget to device out a convension saying which is to hold. Nullity is simple bullshit (please excuse my french). But then again, my own theory will not hold for long, just like Dr James Anderson's theory. Another feasible value of X/0, for any X is i. But i as they every lone know is not a valid number.

RaymondAs someone else in this remark board said, the fact that somebody proposed the special number doesn't do it "real". In fact, it's demonstrably not real because it sits someplace off the real line, in a plane that could live called the "nullity plane", rather akin to the "complex plane" that's composed of the real numbers smooshed together with the value i. Then, of course, you can smoosh nullity, i and the real line every lone together and net something in 3-space that appears very, very extraordinary indeed. It's probably the belt where you can hear one hand clapping, and there are lots of trees falling with no one around to hear them.

Lukosrageif I woke up one day and just made up some nutjob theory, could I live in your word too?

Scott LambEvery calculus student knows the respond to such questions as "what is the restrict of 1/x as x approaches 0 from the right" (positive infinity) and "what is the restrict of 1/x as x approaches 0 from the left" (negative infinity). And more usefully, such questions as "what is the restrict of (f(x+h)-f(x))/h as h approaches 0 from the right" is the definition of derivative. Integrals are defined through limits as well. This is the very foundation of calculus. But "1/0" alone? What does that even mean? There's no answer. It's a dull question. The first thing he wrote - "infinity = 1/0" - was already wrong. If he made his arguments to his peers instead of schoolchildren, they'd shoot him down, and rightfully so. Furthermore, saying that computers cannot divide by zero shows a ridiculous want of common sense. They can consequence anything they design them to do. Many computer number systems beget a special value "NaN" (not a number) that is similar to his nullity concept, except that it's not arrogantly proclaimed as revolutionary or a solution to every problem. Generally, asking a question such as "1/0" indicates a grave logic error. Imagine that airplane needs to cipher the proper elevator trim. Oh, great, the respond is nullity. What does that mean? How should it amble the elevators? Giving this failure condition a original title doesn't change the fact that the airplane's still going to drop out of the sky.

mike in sj, calif.next week, the professor will clarify perpetual motion.

PhilI'm a physicist (not a mathematician). At first glance I feel cautious but at the very time it doesn't seem any worse than the concept of the square root of negative numbers (multiples of i). I'm sure Riemann would beget something to stutter about this. Anderson could beget been a bit less arrogant about it: he's setting himself up for mock if it is shown to live nonsense.

mathmoThis is ridiculous. I can't believe this guy is a professor. Any moron can define division by zero. Here, let R live the set of real numbers. Let / live a binary operation on R that satisfies: (i) 0/0 = 17; (ii) 0/a = 0, for every lone nonzero a in R; (iii) a/b = a * b^(-1), for every lone nonzero a,b in R, where * is the accustomed multiplication and b^(-1) is the multiplicative inverse of b. Too snide Newton and .. Pythagoras (seriously? Of every lone the distinguished mathematicians, Pythagoras?) aren't as smrt as me and Dr Anderson.

/b/rotherhow does i divided by zero, doc?

GabeThe problem of 0/0 or 0^0 is more a problem with 0 then it is with anything else. 0 infinity and negative infinity are slack concepts. In actuality nonexistent of them exist. Zero is just a very very very minute number and infinity is just a very big number in practical terms. There was only ever one upright 0 which was the universe the instant before it exploded and only one upright eternal which is the universe now. Everything else falls into the number line.

DHS1. Let 0/0 = -0- 2. 0^0 = 0^(1-1) 3. 0^(1-1) = 0^1 * 0^-1 4. 0^1 * 0^-1 = 0/1 * 1/0 5. 0/1 * 1/0 = 0/0 6. 0/0 = -0- This guy isn't a genius. Between steps 5. and 6. there should live a step that says "CAN'T DIVIDE BY ZERO!" This guy didn't solve any problem.

Peter RobinsonUsing Dr Anderson's methods. If they assume NULLITY exists then they net 0^1 = 0^(1+0) = 0 * NULLITY = (0*0)/0 = NULLITY. So NULLITY = 0. This is a contradiction, so NULLITY does not exist. To exploit 0/0 you necessity to understand calculus - then l'Hopitals rule tells us that it depends on how you arrive at 0/0, so x/0, 0/x and x/x every lone beget different limits as x tends to zero. The only mystery here is why is Dr Anderson allowed to "teach" this nonsense.

John StandishThis is just bogus. You can't divide by zero. He is just adding another term to math. It would live the very as doing this in code, returning a null object( I am giving a java instance ) private static remonstrate divide(int n, int d){ Objct ret; if(n == 0 || d == 0) ret = null; else ret = (float)n / d; return ret; } try it out. If you print the value of the remonstrate returned by the divide fashion it should either live null or a floating point number. saying that he create the respond is just sad.

He's a liarHe didn't consequence anything. He just came up with a attribute for something he still can't consequence a freaking thing with anyway. every lone he did was deliver us the effort of crashing some computers.

Dr. Alan U. KenningtonIt's every lone very simple really. 0 divided by 0 is the solution of 0.x = 0, which is not unique. The solution is the set of every lone real numbers. You can't consequence much with this, but it is captivating to note that if you extend the real numbers by plus and minus infinity, you can stutter that 1/0 is the set of two numbers plus and minus infinity. But if you subtract these, you get, strangely enough, the set of every lone real numbers. Therefore 0/0 = infinity minus negative infinity. This is every lone very amusing at a primary/secondary school even (which is where I learned it in the 1960s), but every lone very picayune at the undergraduate uni level. Summary: the alleged "nullity" is nonexistent other than the set of every lone real numbers, as every lone mathematicians know.

AnonymousWait, he divided by zero OH SHI-

Garth GrantWe shan't recognize nullity here in California. Some concepts are too nutty even for us.

AnonymousI still fail to observe how this furthers the evolution of their species...

RolfI dunno. I pot concept of 'zero' and imaginary numbers were jeered at then. This may live the case, but I just dunno.

Sågen-Hagénann CromwellianAnything divided by itself is 1. If you divide a pizza by 1, you beget a pizza. If you divde a pizza by 0, you just didn't divide it, and you still beget 1 pizza.

Johnny 99Substituting the "number", nullity, for the word "undefined" brings us no closer to answering what it might live substantive to pick the number zero to the zero-th power. Given the definitions provided in the film, the demonstration shows that the original expression can live easily translated into the penultimate one, yet the final step from zero divided by zero to the soultion, nullity, is not at every lone informative. They already knew their respond was not on the number line. That's why it's undefined. "Defining" nullity as a "number not on the number line" begs the question: what does "a number not on the number line" mean? Given that this 'discovery' is aimed at the problem of digitization, it seems t me that nullity is nothing moroe than an mistake trapping device. Kudos.

PeteySomething about this doesn't sound right. OK been a while since the my days or real analysis but here is my take. If you beget one equation divided by another, if both equations mind to zero then eventually you will net 0/0, but different equations can give different results. e.g. 2x / x , as x goes to zero, you'd contemplate well it is going to 0/0 but its obvious that 2x/x = 2 so the restrict is a real number: 2. Then trivially pick 3x/x, ok as x goes to zero then the finish point (limit) looks like 0/0 but is in fact 3. So here they beget two expressions that finish up as 0/0 but give two different real results when looked at carefully. This is the kindly of reasoning that has led mathematicians to stutter that zero divided by zero is meaningless. Interestingly, computers often determine this situation and give the value as NaN (not a number). But that is just used in mistake checking, so the pute can stutter "Error".

Ya rightInstead of demonstrating it to other maths professors or peers, he shows it to schoolkids. Add it to the long list of fake ass discoveries to net fame list.

anonymouscomputers should not live able to divide by zero, simply because it gives unexpected answers. Its actually much better if the computer throws an error, because you know its doing it wrong.

chrisSo 0/0 is nullity - Big deal, now they beget a label for it. What can you actually consequence with it? It isn't transitive, that's for damn sure.

BanksyAnything is possible. I'm worried that this might unravel time-space, though.

Chuck NorrisI mastered dividing by zero, -infinity years ago!!

Long CatMy anwser may not live entirely birthright due to the fact that I only beget a highschool even math. The problem I find with this is that Dr. Anderson's 'nullity' seems fairly reminiscent of Aleph-null. Which if I'm not mistaken represents every lone numbers.

anoncute trick, Anderson. Now what's (nullity)^(nullity)?

graham pLogically anything divided by nothing still leaves you with the original thing, so I don't know why: n/0 != n ...just makes sense to me anyway.

Michael BurkeLots of people beget argued that this is utter nonsense, as if arithmetic really existed int he real world. Arithmetic (in fact, mathematics), is a set of tools they exhaust to solve problems. (The number "4" for instance, does not exist except as a attribute to delineate a conventional recognition of quantity.) They invented the tools, and sometimes they "don't do sense" but are useful anyway. Non-euclidean Geometry is an instance of a appliance that goes contrary to common sense. On a hypothetical level, this "number" which is identified with the sets of eternal numbers, may beget a real use. So what if it doesn't toil on my glide rule yet.

Todd Allen OsterbergThis is the antique Bill Clinton trick of redefining what the sense of "is" is. If a student makes up an respond out of thin air it is called bunk. If a professor makes up an respond it is called "nullity". So, based upon the transitive property of numbers (if A=B and B=C then A=C), nullity is bunk.

Anonymous PandaThis is complete Garbage. In order for this theory, this man had to approach up with a completely original number, a number that lies -outside- of the number line, therefore, it isn't even a feasible number. Once again, complete garbage.

James DennettSo, nullity = 0/0. But then nullity = (2 x 0) / 0, which is 2 x (0/0), so nullity = 2 x nullity, so nullity = 0. Oh dear, this every lone fails to work. It's not that they don't know how to divide 0 by 0. It's that you can't approach up with an respond without inviting every lone sorts of contradictions. The question is the problem. This picayune nonsense doesn't enable anything original in mathematics or computer science. It's the very kindly of cheap parlour trick mathematicians beget been using forever to "prove" that 1=0.

Vin DieselSo much for "only six people in the universe."

a + b = cI can't find the nullity button on my calculator.

blankWait...zero divided by zero is ...a attribute for zero divided by zero? Gee, that's brilliant! Oh wait...no, it's useless. Zero is not a removable discontinuity, it's a junction point between two number systems, and you're not going to net rid of the fact that it's not properly Part of either (by design, or it would live useless) by making up a crappy attribute for it.

...Does math necessity to net any harder than it is already?

Chuck NorrisI'm sorry people, but I'm the only one who can divide things into no groups. Many people could chop you in half, which is dividing you by 2. I once met a man who could chop you in half at the waist while simultaneously chopping you in half vertically. He divided you by 4. I've known some (few) ninja who could storm you, over time, such that the restrict of the ninja's dividing power as ninja approaches you approached infinity. I don't wish to sound like I am arrogant, but beget you ever met a ninja who could divide you into zero parts? I'm sorry, but the only other being capable of that, other than me, is God so I'm not going to let some professor contemplate he can wreck the laws of physics.

Anonvar foo = 0 var bar = 10 if(foo){ bar / foo }

AnonymousWhat the hell? Pacemakers don't beget computers, so why would it suddenly rule to start doing math?

You fool."square root of -1 (another mathematical problem that creates errors)" - Jon The square root of -1 = "i"... It delves into complicated numbers rather than just having a rational real number or a simple integer as the answer.

LONGCATCan you divide longcat by nullity? dont contemplate so.. If you cant, its completely useless to me...

Dr Anderson4/4 = 1 3/3 = 1 2/2 = 1 1/1 = 1 0/0 = 1 It's that easy. BRILLIANT!

AnonThis is absolutely rediculous. do up a original number because you're too idle to toil around the age antique issue.

Rab ItchanNullity is every lone I contemplate about every day. I sometimes yell myself to sleep thinking how it will never live acceptable mathematics.

Steve HemingwayWell finished the first paper www.bookofparagon.com/Mathematics/PerspexMachineVIII.pdf. They anticipate a number system to behave in a course consistent with their world and nullity is 0 for must of us. Whilst dividing by 0 causes computing errors; they beget consistent ways of processing these and the IEEE NaN (Not a Number), handles things the course they expect. Unfortunately Dr. Anderson create really worse problems as the axioms which split nullity and 0 would desist most computations being what they expect. I got as far as the first two of the 10 extra axioms. Sorry but if {null + a = null} and {-null = null} then a number 'a' equals either null or 0. Result more plane crashes. Anyway nice evening of reading, I must net back now to the more grave glacial fusion experiments!

lol I can invent numbers toolol if 3.14159... is Pi and x/0 is "nullity" then the square root of 2 is hereby known as "omegatron." Its attribute consists of many lines forming a snowflake inscribed in an irregular shape.

RichardI'm hoping this is some sort of joke.... He didn't "solve" anything. Dividing by zero over the real numbers simply wasn't defined. You learn that you can do 0/0 or 0^0 equal anything, in a sense, in an introductory Calculus class! He didn't solve any "unsolved problem in math," he just redefined the real numbers. This wasn't even in an unsolved problem. This is kindly of like saying, "I'm going to do a original number Z which is defined as a number that has the property Z + Z = Z. Now, I beget 2Z = Z, so I divide by Z and solve the unsolved problem of how to do 2 = 1!"

Dan B.The implications of teaching children that dividing by zero is possible, are absolutely terrifying. How can one anticipate to provide them with the mathematical background necessary to outstrip in higher education if your theory is to create numbers? When these children fade out into the real world and are faced with real issues, how consequence you anticipate them to achieve with this kindly of background? If these children want to fade into the sciences and mathematics, this is very destitute preparation. They are in for a rough awakening.

JamesWhen you divide zero by zero the respond is an undefined number because if x = 0\0 then x delineate zero negative infinity positive infinity and every lone the numbers inbetween. The intuition it does not equal anything is because there is no numerical value that can delineate every number. This is an idiotic view and nullity is not a number it's a variable that represents every lone numbers.

beemohThat's Numberwang!

Anon"There are, however, contexts in which division by zero can live considered as defined. For example, division by zero z/0 for z in C^*!=0 in the extended complicated plane C-* is defined to live a quantity known as complicated infinity. This definition expresses the fact that, for z!=0, lim_(w->0)z/w==infty (i.e., complicated infinity). However, even though the formal statement 1/0==infty is permitted in C-*, note that this does not live substantive that 1==0*infty. Zero does not beget a multiplicative inverse under any circumstances." --Wolfram MathWorld I'd pick established rules of calculus over this nonsense any day. Once again: "Zero does not beget a multiplicative inverse under any circumstances."

Mkeyto everyne who says it can no exist because you can't express it in binary, how consequence you express i in binary?

jehanthis guy solved the problem simply because he defined a solution to the problem that's like a student being asked what 0 - 1 is, and responding "booby" saying that "booby" is the result of subtracting one from zero there are no viable mathematical proofs, or applications for this "nullity"

MarkIf the brain is a computer surely watching the video will occasions my head to explode.

AnonymousThe shame of Britain. They even got someone to publish the story. "Hey guys, no solution is now called nullity. GREATEST SCIENTIFIC BREAKTHROUGH EVER." every lone he did was give a special attribute to 0/0. He has not solve any problems. If I still cannot solve the celebrated 2 = 1 problem, then this man has done NOTHING. You necessity to divide by zero to prove 2 = 1.

Captain ObviousYou can't divide by zero! The Universe will implode!

GergeI LIKED attempting to divide by 0.

1/0This is profoundly stupid. They couldn't device it out, so they gave their ignorance an official label and claimed it was the answer. It still doesn't give any kindly of meaningful answer, and it has no practical application of any sort. This fails massively.

The UniverseI warned you guys not to divide by zero. Now you're gonna net swallowed by a black hole.

ObserverSo...why spread the word in a lofty school and on TV? Shouldn't you live publishing in a paper somewhere? net it down in writing where someone can give you credit for it, if they actually believe you.

Oh dear...What's the first step in his derivation? 1/0 = infinity. He's used what he's trying to prove in his proof. Cyclic arguments are acceptable only as proof of contradiction, and only when the definition is proved wrong...

ThomasThis should beget been shown to degree and/or A even students, NOT junior schoolkids, who beget a nasty tendancy to absorb whatever is thrown at them (we've every lone been there) Anybody can do up a title for a number, and im still fond of the 1/0 = infinity theory (although both sides of undefined, a problem indeed)

AnonymousWaitaminnit is nullity ONLY 0/0 or would any other number work? Also, division by zero has always been possible, google the time dilation equation.

0rionYou know, math really IS facile if you simply rule that there's a original rule and start making stuff up from there. ...And why exactly would a pacemaker live forced to divide something by zero?

AnnonymousI understand what he is saying and it does toil - in theory. But every lone he has proved is that they can do up imaginary numbers to solve problems that cannot live solved in real life but thats already been done before and when will this live of use? The day they discover the sixth dimension maybe.....

Prof. Richie McRichstonsonThis is quite possibly the best mathematical solution ever found!

UK AnonymousThis can't live sanguineous right, there must live a mistake. It's not feasible to divide by zero, it'd extinguish the entire Earth.

Black WyvernThat was complete mathematical herecy. The number line may not live a circle, that's just a piece of theory that didn't uphold solve the problem. IMO, solving this problem with reciprocals is a better idea. 1/x = a fraction nearby to zero. 1/infinity would live zero, theoretically. So they set up the reciprocal triange with that. .....1 ....----.. .0...|...Infinity From that they can observe the relationship between 0, 1 and Infinity. 1/0 = Infinity This is a course better fashion than some dull theory. Just so you know it works: .....2 ....----.. .3...|...2/3 2 divided by 3 = 2/3 3 x 2/3 = 2 2 divided by 2/3 = 3 Any 2 positive numbers should consequence that.

Steve IrwinI divided by zero, and nullity didn't uphold me. AT ALL.

BobThe problem with this "new number" that "[stretches] from negative infinity, through zero, to positive infinity," that will supposedly allow computers to grasp x/0, is that ANY equation can equal nullity. 1+1=nullity, 3*-3=nullity, etc. So unless you hard-code every programing language to only exhaust this number in the event of dividing by zero, it will occasions errors in any math problem. And then, stutter you beget a flight computer, as the above article suggests, that needs to divide by zero, and then add 100, and that's how many yards it has left till it hits the ground. x/0+100=nullity, so it has anywhere between infinity and negative infinity until it crashes. That really narrows it down, huh? Now instead of the program getting syntax error, which will quit out of the program with an mistake message, the program gets a ratiocinative error, as it will attempt to exploit a totally worthless number. What will the program assume? It's eternal miles away from the earth? It's eternal miles under the surface? Somewhere in between? The program wont crash, but the plane sure as hell will.

DomMy mobile (SPV C600) does in fact devide by 0. It gives an respond of "0"

DavidThis is obviously a hoax, or something extremely dull and irrelevant. How would you delineate this in binary? Surely it's just algebraic. Is more like adding a word to the English language than solving a math problem.

Prof. Bakerany real number divided by zero does not exist. the pupils that beget been taught this are now more dull from being in dr anderson presence. this should never live taught in schools...EVER!

pbeThis must live hoax. No mathematician could stutter that this theory works or is usable. It is stated in the article that nullity is numbers from -infinity to +infinity but this is just not feasible - infinity is not a number but an expression for any given amount of MORE numbers. So nullity cannot live defined as a number. This does not solve anything ether - every lone they could consequence is to change division by zero exception in their apps to nullity exception and still finish up with the very solution.

TonySurely however as any number divided by itself is one this is too the very for zero and not nullity?!

XeroOkay, I barly understand but what the hell are the doing!

FredIT MUST live A HOAX. One of the clues is the mention of Pythagoras: he was around much before 1200 years ago, and as far as I remember, the ancient Greeks did not know zero!

Hubert J. againNow that I watched the video, it's not even that! Heck, what I just said made more sense than that... What he wrote on the board: 0/0 = -0- (assuming true) 0^0 = 0^(1-1) = 0^1 * 0^-1 = 0/1 * 1/0 = 0/0 = -0- That's not a proof. That's just the very arbitrary definition he started with! "I assume that 0/0 is nullity. 0^0 is nullity. Therefore, nullity is a original number." No, it's still just 0/0. This is just a original amusing attribute to stutter the very thing; Pythagoras, Fermat, and Riemann are rolling in their graves... laughing at this buffoon.

hannahha im in the front row. it was fun and they got to miss a lesson. yum

DanThats just stupid. How does that uphold in any way? What are the properties of this made up value? How can you exhaust them? saying that dividing by 0 results in infinity is more useful than this. If I beget ten apples and I divide them amongst zero people, each person gets how many apples? ZERO! Therefore anything / 0 = 0. Just stupid.

Mark WThere're plenty of books on infinity (not eternal mind you ;-) and they accommodate such definitions e.g. capitalised omega to delineate infinity to the power infinity. This strikes me as more marketing than mathematics!

Pierre KeeleDr Bedford would explode with enrage if he saw this. Is this man a Dr of Philosophy and not Mathematics?! I observe he is from the computer science department, has he never studied the laws, lemmas and definitions of Mathematics. You consequence not prove something by just inventing a original word.

Fred0 to the power of 0 equals 1 (try it on your calculator). Therefore, nullity equals 1. QED

anonymousEveryone knows that when you divide by zero it's OVER NINE-THOUSAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAND Seriously, this is the most useless solution yet: instead of getting an mistake message you net nullity , which doesn't uphold more than the mistake message

FredSounds like a hoax. Does not solve anything at all. If so, how consequence you write nullity in binary ???

JillDo I understand Dr Anderson's theory? Not a word

AnonymousSTOP TRYING TO extinguish THE UNIVERSE! YOU'RE MAD DOC, MAD!!

BrianSounds interesting. Too snide the videos are in real Player which ruins your computer worse than diving by zero so i won't watch them.

Prof. Hubert J. FarnsworthAll he did is give a title to the opposite pole of a non-Euclidean, spherical geometry. He tied the two "ends" of the number line together to do a loop. And I'm fairly sure non-Euclidean geometry is not new.

PhilThis is absolutely ridiculous. Dividing by zero is completely unnecessary AND impossible. It can't live imagined (as a root of -1 can).

caskai hope i am not wrong, but my understanding is that basically he is telling people to observe the number 0, not as a number but as a concept of nothingness in which case, i consequence observe computers and aplications capitalize from it, in the logicla sens eof which computers toil at the moment, when they approach up to divide by zero they fail becuase that is how they beget always programed them to live but if they now recommend the computer 0 is not a number of value, but a variable of the concept nothingness, then they could over approach many situations when they coudl formulate and beget variables of no exhaust or no avaliability.. the thing is, computer would eb able to "rationalize" on the 0 divisions, becuase they would deal the variable as a non existant of data, and still carry on the procces, instead of looping out in error... consequence i do sense? o.O

Mitchell H.Ryan, whatever you're on, I want some of it.

AnonymousBlack holes, everywhere. Nice job, Dr. Anderson.

AnoymousCANNOT DIVIDE BY ZERO!!!!!111oneoneone

TiodeSo, what? He just made up a original number because he got frustrated not being able to toil it out?

Thomas ChapmanHe has not 'solved' anything - he has just given an existing result a name. This won't 'fix' a flight computer either - it doesn't change anything.

AnonymousI submit a original number based on this nullity breakthrough: infinullity. Infinullity is the number that results when one divides infinity by zero. I anticipate that it will live just as useful as nullity itself. Seriously though, I don't know much about pacemakers or autopilot algorithms, but if either actually performs division, one would contemplate it would comprise some profile of exception handling for the case of dividing by zero already.

Chris CroughtonI feel sorry for those children when they find out that computers beget been happily handling such operations for decades. The value NaN ("Not a Number") is generated by exactly that kindly of invalid operation, like zero raised to the power zero. It even comes in both positive and negative forms! And computers happily exploit the results of using it in subsequent calculations, and will generate traps so that the mistake can live automatically corrected (and so don't crash and "fail to start in the morning" like his car example).

George BushThis is absurd, you can't just pick two unknown quantities and set them to your own made up definition. I would like to observe this "genius" approach up with a course for this magical number to live represented in binary

AnonymousWhat has science done?

Patrick BamptonWhat is a RAM auto file? Why not present the explanations in html or pdf format. Then I might live able to read them.

noonnecalling 0/0 nullity gives you nothing, its by far not as smart as calling sqrt(-1)=i... they beget to note how to consequence some (new!!!) maths with it.

Anonymoushis biggest mistake is assuming 1/0 is infinity and -1/0 is negitive infinity, which it is not, its its own seperate entity. 1/0 is essentially unitless much in the course zero is

Peter HDr. Anderson claims that 1/0 = infinity -1/0 = negative infinity 0/0 = nullity 0/0 = (0/1) * (1/0) = 0 * infinity = nullity so 0 * infinity = nullity, right? But, if 1/0 = infinity, then it stands that infinity * 0 = 1 thus 1 = nullity? I fail to observe how this view could withstand basic algebra.

Chris CroughtonThat 'theory' is total rubbish. every lone he has done is supplant "zero divided by zero is indeterminate" (it can live anything from zero to infinity, depending on how it is derived) but "I'm going to exhaust this attribute for it", which doesn't alter anything. He didn't "solve the problem", he merely said "I'm going to muster the respond 'nullity'" and trivially dismissed the actual problem (which is that "zero divided by zero" is as meaningless as "this statement is false").

JonathanIt's a distinguished idea, but he shouldn't net credit for "discovering" something.... if i where to do up a attribute for the square root of -1 (another mathematical problem that creates errors) should I net some kindly of global recognition for my genius? no, it's just a profile of shorthand or short cut. nothing great. -Jon

Captain Homothe view of 0/0= -0- (or however it would look) is stupid. if they beget (0*x)/0 = (0*5)/0 0/0 * x = 5 * 0/0 then -0- * x = 5 * -0- | : -0- x=5 but in reality that just doesn't work.

AnonO.O Devision by zero IS possible!

darkdoomerdivide anything by nothing, you'll still beget nothing divised, so, no changes. marons.

Atif HassanIts good. But I contemplate there is nothing original or special about it. Its obvious. but what problem has been solved? infinity is always there.

RyanI thought of that number months ago and beget approach up with an unconventional "number circle" to uphold clarify it better. This was a short text file i created a while back to clarify it: "The "Number Line" that they every lone learned in school in not actually a line, but a circle. The top of the coterie is 1, the bottom of the coterie is -1, the birthright side of the coterie is 0, and the left side of the coterie is a number they beget yet to define. This number is the number birthright between negative infinity and infinity, but on the opposite side of the coterie as 0. The coterie is set up so that the negative of any positive number is on the exact opposite side of the coterie over the horizontal axis and the inverse of any number is on the opposite side of the coterie over the upright axis. This means that 0 which can live written as 0/1 has an inverse over the upright axis of the undefined number which can live written as 1/0. Anytime in calculus when you net a upright asymptote, it is actually equal to the undefined value 1/0. This means that the expression 1/0 does indeed exist, but has yet to live defined by modern mathematics."

Robin AnderssonDr Anderson beget not solved anything, just ignored it. Making a original number out of nowhere doesn't do it real.

Jimmy Hamilton-BrownI contemplate I understand it - but I am not sure what they beget gained apart from a original attribute which is not on my computer - approach to contemplate of it nor is infinity!

zahrahunfortuanately i could not view it on the internet, i contemplate from what i saw on the tv, was quite impressive.

zerooooooa original number? AMAZING!

R PageDr Anderson's theory is explained well, but it would more useful if the film allowed viewers to observe what he was writing on the board.

John NolanSo if my original pacemaker divides by zero, I won't die? How will that toil then? I've watched the prof's video, but can't quite toil that one out...

Samin the derivation when the expression 1/0 x 0/1 is written isn't the 1/0 undefined and the solution unattainable?

MeOoh, I just saw this on the news, and :o oo strange.

### Using the Jtable | killexams.com real questions and Pass4sure dumps

In Parts 1 and 2 of this article (JDJ, Vol. 6, issues 1 and 7) I discussed how to exhaust a JTable with a table model and showed how much toil is involved getting a JTable to toil with data. This is quite a departure for veterans of other fourth-generation languages who may live used to developing in Visual Basic or PowerBuilder.

Both these languages beget knowing controls that reserve track of the data as the user is manipulating it. These controls can then determine how to exploit database changes such as inserts, updates, and deletes. Java doesn't beget any built-in functionality. remember the antique Java adage: "To exhaust it you must first build it."

Remember that the JTable or the table model is in no course connected to the database. Even when you're instantiating the JTable based on its table model, the model simply populates a collection (usually vectors), then passes them back to the JTable. Any necessary functionality must live programmed to exhaust the JTable to achieve actual database manipulation.

It would live nice if a JTable or its associated model had a fashion called Update(). Unfortunately, it doesn't, at least not yet. With a bit of work, by the finish of this article you should live able to program such a method. Before I discuss the login needed for real database updates, I'll discuss the groundwork involved. Primarily, how can the JTable and table model live configured to detect user changes and how to add and delete rows. When these three tasks can live accomplished, only then can the database live updated.

I'll walk through the steps needed for database updates. Listing 1 provides the complete code, and device 1 displays the application (Listings 1-9 can live create on the JDJ Web site, www.sys-con.com/java/sourcec.cfm.)

Detecting User ChangesWhere consequence they start? Before they can contemplate about updating a database, the table model must first live conscious of user changes. In case you haven't noticed, by default the JTable and associated table model don't apply any user-supplied changes. For example, if a cell value is "Cheeseburger" and the user types "Hotdog" over it, the original value is displayed only when that current cell has the focus. As soon as the user tabs to another cell, the antique value is restored. This is not a bug. Remember, the programmer is amenable for every lone behavior. The antique value is restored because no code exists to stutter otherwise.

How can they net the original value to remain in the cell? By coding the setValueAt() fashion in the table model. This fashion from the Table- Model class is automatically fired when the contents of the cell are modified and the focus is changed to another cell. This fashion tells us the row, column, and original value of the cell. Then code has to live written to update the data (in their case vectors) that do up the table model. In Listing 2, the vectors that do up the table model are updated with the original value for the cell.

Adding RowsAny suited user interface has the functionality to add rows. Any GUI you write using a JTable should comprise it. But where can this functionality live added? Remember, the JTable is merely the view of the data. Most functionality, including the addition of rows, must occur in the table model. With that in mind, there should live a fashion called addRow() or insertRow(), for example, available for the table model, right? Guess again. Such methods must live programmed. If you contemplate about it, the absence of such built-in Java methods makes sense. To understand why, you must first observe what a "row" really is.

Because the table model contains the data for the JTable, it too controls and is conscious of what a row looks like. The JTable is pretty oblivious to both these facts. A "row" in a table model can and will behold very different from application to application. For example, Application 1 may beget three columns with the data types string, integer, and boolean. Application 2 may beget four columns with the data types string, string, float, and integer. The concept of a "row" really exists only for the beholder. As far as Java is concerned, a row is a vector of supporting classes. The data types for these classes are as varied as the fantasy of the programmer who created them. Because of this variation there's no built-in Java fashion to insert or add a row to a table model, because Java doesn't reserve track of what a row looks like. This is the responsibility of the programmer.

In their example, a row in a table model is made up of a vector. Each constituent within the vector reflects the data type of the database column retrieved into it. To add or insert a row, the vector must first live queried about what data types it contains. These data types can then live built and added into another vector. This resulting vector can then live added to their table model, effectively adding a row. Listing 3 demonstrates how to add a row to the table model. For brevity, only vectors containing strings, integers, and booleans can live added.

Deleting RowsFortunately, deleting rows in the table model is a bit less challenging. Deleting is fairly facile because it's irrelevant which data types the row consists of. The only real concern is to remove the row from the table model. However, the deleted row needs to live remembered in some course when they try to delete it from the database.

When the database is updated, SQL DELETE statements will beget to live built. Even when the row no longer exists in the table model, the primary key for the deleted row must live remembered so the corresponding record in the database can too live deleted. This is accomplished by saving the primary key for the deleted row into a vector.

Later, when they build the SQL DELETE statement, they can require the vector to recommend us which row to delete. For simplicity, Listing 3 assumes the primary key is numeric and is the first column in the row. With a bit of ingenuity, this functionality can live expanded to comprise any number of columns with any data type. Listing 4 illustrates how to delete a row from a table model, but remember its primary key. This simple fashion deletes a row from within the vector and notifies the JTable to update the view - making the row removal visible to the user.

Updating the DatabaseNow for the fun part. So far their table model can exploit data modifications, original rows, and deleted rows. The next step is to apply the changes to the database. Since the table model and the database don't know about each other, it's up to the programmer to determine how the database will live affected. The concept of applying changes to the database is simple - create and execute a SQL statement. Depending on the status of the row in the table model, a SQL INSERT, DELETE, or UPDATE statement needs to live built. Sounds easy? Well, it is. The hard Part is writing the code that will build the SQL. Once the code is built, database transactions are a snap. The next section will discuss and demonstrate the code needed to generate SQL statements.

GroundworkBefore the code can live written to generate SQL, a few housekeeping chores are in order. Information such as the primary key, names of the columns in the database, and a user-entered value from the table model must live obtained. The primary key, as well as the database column names, can live retrieved through Java metadata methods. For simplicity, this table model will assume that the first column in each row is the primary key and the data type is numeric. Listing 5 keeps track of how many rows are in the table model, what the user-entered values are, and the value for each of the primary keys for each row.

At this point code needs to live written that will achieve two loops. First, the code loops through each row of the table model, then through each constituent within the row. remember that rows within the table model are really collections of other objects (e.g., strings and integers). Each constituent within the row must live queried for its value, data type, and whether it contains the value for the primary key.

When testing each column for its data type, you can start saving the user-supplied values to live used in the SQL. Data type is very valuable because it changes the course the program keeps track of the user-entered values. For example, if the user changes a column of the data type STRING, the program must wrap lone quotes around the value, otherwise the SQL statement will fail. Listing 6 queries the elements in each row for three different data types. For simplicity, this instance doesn't test for every lone feasible types; this modification is simple once you understand the basics.

Performing the INSERTNow that they beget data describing each column - as well as the data itself - code can live added to INSERT rows in the database, basically creating and executing a SQL INSERT statement. First, the vector that contains every lone the original row numbers is queried as to how many entries it contains. If it contains any entries, the row number in the vector is compared to the current row number in the table model. If the row matches, the SQL statement can live built. Listing 7 loops through every lone the columns and data values and builds the SQL INSERT statement. After the statement is built, it's executed against the database. If every lone goes well, the original row is now saved.

Performing the UPDATEIf the current row has not been inserted, a SQL UPDATE statement is built. Listing 8 obtains the title of the database column as well as its value. After the UPDATE statement is created, it's executed against the database. The record has now been updated.

Performing the DELETEDeletes toil a cramped differently. Since the row no longer exists in the table model, there won't live any current row to loop through. When the row was deleted from the table model, the primary key of the row was saved in a vector. When deleting a row in a database, the column names and the data values are irrelevant. every lone that's needed is the primary key. Listing 9 obtains the key for deleted rows and builds a SQL DELETE statement. Also, for the sake of brevity, this code assumes that the record being deleted has no alien key constraints. If it does, the DELETE statement would fail, of course.

Final ConsiderationsNow that wasn't too bad, was it? The tricky Part was creating the SQL statements. As a disclaimer I'd like to point out that the code in this instance has been simplified in order to demonstrate the basics of how to exhaust the JTable and associated table model to deliver changes to the database. For example, this article doesn't pick into consideration SQL errors that can occur when violating a database constraint. Also, row management would live better served by using hashtables to hold the status of each row as well as the primary key value. In any event, the code is functional and generic enough for exhaust in most projects. Feel free to exhaust and help it as you observe fit.

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ACI [3 Certification Exam(s) ]
Acme-Packet [1 Certification Exam(s) ]
ACSM [4 Certification Exam(s) ]
ACT [1 Certification Exam(s) ]
Admission-Tests [13 Certification Exam(s) ]
ADOBE [93 Certification Exam(s) ]
AFP [1 Certification Exam(s) ]
AICPA [2 Certification Exam(s) ]
AIIM [1 Certification Exam(s) ]
Alcatel-Lucent [13 Certification Exam(s) ]
Alfresco [1 Certification Exam(s) ]
Altiris [3 Certification Exam(s) ]
Amazon [2 Certification Exam(s) ]
American-College [2 Certification Exam(s) ]
Android [4 Certification Exam(s) ]
APA [1 Certification Exam(s) ]
APC [2 Certification Exam(s) ]
APICS [2 Certification Exam(s) ]
Apple [69 Certification Exam(s) ]
AppSense [1 Certification Exam(s) ]
APTUSC [1 Certification Exam(s) ]
Arizona-Education [1 Certification Exam(s) ]
ARM [1 Certification Exam(s) ]
Aruba [6 Certification Exam(s) ]
ASIS [2 Certification Exam(s) ]
ASQ [3 Certification Exam(s) ]
ASTQB [8 Certification Exam(s) ]
Autodesk [2 Certification Exam(s) ]
Avaya [96 Certification Exam(s) ]
AXELOS [1 Certification Exam(s) ]
Axis [1 Certification Exam(s) ]
Banking [1 Certification Exam(s) ]
BEA [5 Certification Exam(s) ]
BICSI [2 Certification Exam(s) ]
BlackBerry [17 Certification Exam(s) ]
BlueCoat [2 Certification Exam(s) ]
Brocade [4 Certification Exam(s) ]
Business-Objects [11 Certification Exam(s) ]
Business-Tests [4 Certification Exam(s) ]
CA-Technologies [21 Certification Exam(s) ]
Certification-Board [10 Certification Exam(s) ]
Certiport [3 Certification Exam(s) ]
CheckPoint [41 Certification Exam(s) ]
CIDQ [1 Certification Exam(s) ]
CIPS [4 Certification Exam(s) ]
Cisco [318 Certification Exam(s) ]
Citrix [47 Certification Exam(s) ]
CIW [18 Certification Exam(s) ]
Cloudera [10 Certification Exam(s) ]
Cognos [19 Certification Exam(s) ]
College-Board [2 Certification Exam(s) ]
CompTIA [76 Certification Exam(s) ]
ComputerAssociates [6 Certification Exam(s) ]
Consultant [2 Certification Exam(s) ]
Counselor [4 Certification Exam(s) ]
CPP-Institue [2 Certification Exam(s) ]
CPP-Institute [1 Certification Exam(s) ]
CSP [1 Certification Exam(s) ]
CWNA [1 Certification Exam(s) ]
CWNP [13 Certification Exam(s) ]
Dassault [2 Certification Exam(s) ]
DELL [9 Certification Exam(s) ]
DMI [1 Certification Exam(s) ]
DRI [1 Certification Exam(s) ]
ECCouncil [21 Certification Exam(s) ]
ECDL [1 Certification Exam(s) ]
EMC [129 Certification Exam(s) ]
Enterasys [13 Certification Exam(s) ]
Ericsson [5 Certification Exam(s) ]
ESPA [1 Certification Exam(s) ]
Esri [2 Certification Exam(s) ]
ExamExpress [15 Certification Exam(s) ]
Exin [40 Certification Exam(s) ]
ExtremeNetworks [3 Certification Exam(s) ]
F5-Networks [20 Certification Exam(s) ]
FCTC [2 Certification Exam(s) ]
Filemaker [9 Certification Exam(s) ]
Financial [36 Certification Exam(s) ]
Food [4 Certification Exam(s) ]
Fortinet [12 Certification Exam(s) ]
Foundry [6 Certification Exam(s) ]
FSMTB [1 Certification Exam(s) ]
Fujitsu [2 Certification Exam(s) ]
GAQM [9 Certification Exam(s) ]
Genesys [4 Certification Exam(s) ]
GIAC [15 Certification Exam(s) ]
Google [4 Certification Exam(s) ]
GuidanceSoftware [2 Certification Exam(s) ]
H3C [1 Certification Exam(s) ]
HDI [9 Certification Exam(s) ]
Healthcare [3 Certification Exam(s) ]
HIPAA [2 Certification Exam(s) ]
Hitachi [30 Certification Exam(s) ]
Hortonworks [4 Certification Exam(s) ]
Hospitality [2 Certification Exam(s) ]
HP [746 Certification Exam(s) ]
HR [4 Certification Exam(s) ]
HRCI [1 Certification Exam(s) ]
Huawei [21 Certification Exam(s) ]
Hyperion [10 Certification Exam(s) ]
IAAP [1 Certification Exam(s) ]
IAHCSMM [1 Certification Exam(s) ]
IBM [1530 Certification Exam(s) ]
IBQH [1 Certification Exam(s) ]
ICAI [1 Certification Exam(s) ]
ICDL [6 Certification Exam(s) ]
IEEE [1 Certification Exam(s) ]
IELTS [1 Certification Exam(s) ]
IFPUG [1 Certification Exam(s) ]
IIA [3 Certification Exam(s) ]
IIBA [2 Certification Exam(s) ]
IISFA [1 Certification Exam(s) ]
Intel [2 Certification Exam(s) ]
IQN [1 Certification Exam(s) ]
IRS [1 Certification Exam(s) ]
ISA [1 Certification Exam(s) ]
ISACA [4 Certification Exam(s) ]
ISC2 [6 Certification Exam(s) ]
ISEB [24 Certification Exam(s) ]
Isilon [4 Certification Exam(s) ]
ISM [6 Certification Exam(s) ]
iSQI [7 Certification Exam(s) ]
ITEC [1 Certification Exam(s) ]
Juniper [63 Certification Exam(s) ]
LEED [1 Certification Exam(s) ]
Legato [5 Certification Exam(s) ]
Liferay [1 Certification Exam(s) ]
Logical-Operations [1 Certification Exam(s) ]
Lotus [66 Certification Exam(s) ]
LPI [24 Certification Exam(s) ]
LSI [3 Certification Exam(s) ]
Magento [3 Certification Exam(s) ]
Maintenance [2 Certification Exam(s) ]
McAfee [8 Certification Exam(s) ]
McData [3 Certification Exam(s) ]
Medical [69 Certification Exam(s) ]
Microsoft [368 Certification Exam(s) ]
Mile2 [2 Certification Exam(s) ]
Military [1 Certification Exam(s) ]
Misc [1 Certification Exam(s) ]
Motorola [7 Certification Exam(s) ]
mySQL [4 Certification Exam(s) ]
NBSTSA [1 Certification Exam(s) ]
NCEES [2 Certification Exam(s) ]
NCIDQ [1 Certification Exam(s) ]
NCLEX [2 Certification Exam(s) ]
Network-General [12 Certification Exam(s) ]
NetworkAppliance [36 Certification Exam(s) ]
NI [1 Certification Exam(s) ]
NIELIT [1 Certification Exam(s) ]
Nokia [6 Certification Exam(s) ]
Nortel [130 Certification Exam(s) ]
Novell [37 Certification Exam(s) ]
OMG [10 Certification Exam(s) ]
Oracle [269 Certification Exam(s) ]
P&C [2 Certification Exam(s) ]
Palo-Alto [4 Certification Exam(s) ]
PARCC [1 Certification Exam(s) ]
PayPal [1 Certification Exam(s) ]
Pegasystems [11 Certification Exam(s) ]
PEOPLECERT [4 Certification Exam(s) ]
PMI [15 Certification Exam(s) ]
Polycom [2 Certification Exam(s) ]
PostgreSQL-CE [1 Certification Exam(s) ]
Prince2 [6 Certification Exam(s) ]
PRMIA [1 Certification Exam(s) ]
PsychCorp [1 Certification Exam(s) ]
PTCB [2 Certification Exam(s) ]
QAI [1 Certification Exam(s) ]
QlikView [1 Certification Exam(s) ]
Quality-Assurance [7 Certification Exam(s) ]
RACC [1 Certification Exam(s) ]
Real-Estate [1 Certification Exam(s) ]
RedHat [8 Certification Exam(s) ]
RES [5 Certification Exam(s) ]
Riverbed [8 Certification Exam(s) ]
RSA [15 Certification Exam(s) ]
Sair [8 Certification Exam(s) ]
Salesforce [5 Certification Exam(s) ]
SANS [1 Certification Exam(s) ]
SAP [98 Certification Exam(s) ]
SASInstitute [15 Certification Exam(s) ]
SAT [1 Certification Exam(s) ]
SCO [10 Certification Exam(s) ]
SCP [6 Certification Exam(s) ]
SDI [3 Certification Exam(s) ]
See-Beyond [1 Certification Exam(s) ]
Siemens [1 Certification Exam(s) ]
Snia [7 Certification Exam(s) ]
SOA [15 Certification Exam(s) ]
Social-Work-Board [4 Certification Exam(s) ]
SpringSource [1 Certification Exam(s) ]
SUN [63 Certification Exam(s) ]
SUSE [1 Certification Exam(s) ]
Sybase [17 Certification Exam(s) ]
Symantec [134 Certification Exam(s) ]
Teacher-Certification [4 Certification Exam(s) ]
The-Open-Group [8 Certification Exam(s) ]
TIA [3 Certification Exam(s) ]
Tibco [18 Certification Exam(s) ]
Trainers [3 Certification Exam(s) ]
Trend [1 Certification Exam(s) ]
TruSecure [1 Certification Exam(s) ]
USMLE [1 Certification Exam(s) ]
VCE [6 Certification Exam(s) ]
Veeam [2 Certification Exam(s) ]
Veritas [33 Certification Exam(s) ]
Vmware [58 Certification Exam(s) ]
Wonderlic [2 Certification Exam(s) ]
Worldatwork [2 Certification Exam(s) ]
XML-Master [3 Certification Exam(s) ]
Zend [6 Certification Exam(s) ]

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