Talk:Division by zero

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Directional Limits and 0+[edit]

When one is evaluating the limit lim x->0+ (1/x) = +infinity, although it's intuitively reasonable to think of the limit as lim x->0+ (1/x) = 1/0+ = +infinity, that is not technically correct, since 0+ is not a number, and so you can't divide by it. I ran across someone today who was misled by this, so I corrected the page to fix it. Twiffy (talk) 02:07, 10 June 2011 (UTC)

1/0+ is no more than a shorthand way of writing lim x->0+ (1/x). But you may be right that this notation can confuse some readers, and is best omitted. FilipeS (talk) 14:21, 6 February 2012 (UTC)

0/0 = 1, obviously...[edit]

The function x/x = 1 for every x on the complex plane, with a tiny, point sized hole of WTF? at zero. That says you can get arbitrarily close to zero, and the value of x/x is still 1. Madkaugh (talk) 21:32, 10 August 2009 (UTC)

The function (2x)/x = 2 for every x on the complex plane, with a tiny, point sized hole of WTF? at zero. That says you can get arbitrarily close to zero, and the value of (2x)/x is still 2. —JAOTC 05:05, 11 August 2009 (UTC)
Indeed it is. But you introduced an additional factor:
(2x)/x = 2(x/x) =* 2(1) = 2
(allowing that you can get arbitrarily close ...)
I said one is one, you said two times one is two. I say tomato, you say catsup is a vegetable ... Madkaugh (talk) 00:27, 12 August 2009 (UTC)
My point is that a fraction is not guaranteed to approach 1 as x approaches 0, just because the numerator and denominator both approach 0. For the fraction to approach 1, we need the numerator and denominator to approach 0 in the same way (like x/x), and there's no such information in the expression "0/0". Taking 0/0 to mean the limit of x/x, discarding any other limit of the form 0/0, is completely arbitrary. (We have an article about this at indeterminate form.) —JAOTC 05:14, 12 August 2009 (UTC)
Good point. Madkaugh (talk) 02:06, 13 August 2009 (UTC)

Also the function f(x=)sin(x)/tan(x) proves that 0/0=1. —Preceding unsigned comment added by (talk) 18:39, 18 October 2009 (UTC)

Actually, the function f(x)=sinx/tanx can be rearranged into f(x)=(sinx)*(cosx/sinx), at which point is simplified to f(x)=cosx. The only thing you're proving is that cos(0)=1. — Preceding unsigned comment added by (talk) 21:28, 16 December 2011 (UTC)
As mentioned in the article, see L'Hopital's Rule for how to, in general, handle two functions g(x)/h(x), when both g(x) and h(x) yield 0 at x=0. The solution has been around for over 300 years. Bill Wvbailey (talk) 23:06, 16 December 2011 (UTC)
hmm... lets assume z=0. if z/z=x, then in theory x=1. yet if z=0, then 0/z=x, and then x=0. so, x would equal 1 OR x would equal 0, in the same manner as y equals 2 OR -2 when y equals the square root of 4 Didlybob123 (talk) 03:43, 27 February 2013 (UTC)

You can divide by zero[edit]

.. when it becomes necessary to do so. The universe does it all the time. Here's an article: Dirac delta function - it crops up in discrete probabilities expressed as integrals and in signal processing. Madkaugh (talk) 21:32, 10 August 2009 (UTC)

Evidently Chuck Norris does it all the time too.
(I actually went to this article looking for that tidbit, but found it on Chuck Norris facts).
Actually, the Dirac delta function doesn't give you a way to divide by zero. That's simply a zero-width function having a finite integral. It's a construct. There are plenty of seeminly contradictory things in mathematics; for example if you rotate the curve y=1/x around the x axis from 1 to infinity, you get a trumpet-shaped surface that has a finite volume but infinite area; in other words you can fill it with paint but you can't paint it.
There are also examples like y=sin(x)/x that blow up mathematically when x=0, but actually have a value there. sin(x)/x=1 as x goes to 0. ~Amatulić (talk) 19:58, 1 December 2009 (UTC)
...are you suggesting that we mention these things (black hole, Dirac delta function) in the article? If so, that's a good idea; feel free to go ahead and add them.
As for the Chuck Norris fact, I think it was considered not notable enough for this article. --Zarel (talk) 10:40, 2 December 2009 (UTC)

It is possible to divide by zero in real life situations, let us say that I have 5 sweets. When explaining division you use the sharing example, right? So, if I were to divide by one, a single person would gain the whole quantity of the object/s. When dividing by zero, you still have to give away all of the quantity/objects but there is not a person! It's almost as if you're putting it in the trash, but in maths' formulae you cannot get rid of the complete quantity without subtraction, so the calculator cannot process it. In other words dividing by zero is sharing with nobody but you're still willing to share so you keep none. Hope that clarified everything. (talk) 20:44, 26 July 2012 (UTC)

I'm not sure that's quite accurate. the truth is, we don't really know a real life aplication for divided by zero concepts, but that doesn't mean their isn't one. I believe that dividing by zero is possible in some cases, but the idea that dividing 5 cookies into 0 groups is the same as throwing away the cookies wouldn't be dividing by zero, but more along the lines of giving your cookies to the trash can. this situation would be 5/1, not 5/0. (talk) 02:28, 28 February 2013 (UTC)

0/0 = x, fact[edit]

I know I've said this before but I think I might of thought of some proof that can end all of this division by zero shit forever. For those who don’t know what logarithms are, log(a) b is the same as saying "With a^x, what does x have to be to get b?". Lets look at log(2) 256 as an example, with 2^x, what does x have to be to get 256? The answer is 8, because 2^8 = 256. Now lets look at log(1) 1, with 1^x, what does x have to be to get 1? x can of course be any number, so I will just keep the answer as x. Because log(a) b = log b/log a (with log being log(10), it still works the same with any other positive logarithm) we get

x = log(1) 1 = log 1/log 1 = 0/0

We can use a similar method to prove that 1/0 doesn't have an answer, with 1^x, what does x have to be to get 10?

log(1) 10 = log 10/log 1 = 1/0

If you don’t understand the above proof you can get the same answers by asking "If you are travailing at 0mph, how long does it take you to travel 0 meters?" or simply "How many 0's go into 0?" for 0/0 and "If you are travailing at 0mph, how long does it take you to travel 1 meter?" or "How many 0's go into 1?" for 1/0. Well okay maybe 'x' isn't a suitable answer for the first one, but you have to at least accept that the answer can be any number, and that it deserves at least a small mention in this article. Robo37 (talk) 15:32, 12 August 2009 (UTC)

I fail to see how this differs from what you wrote above. The answer is the same: we want 0 divided by 0 to be a number, a single number. If we can't define it that way, it's not very useful to define it at all. You are definitely right that the correct way to define it if we thought it useful would be as an entity that assumes all possible values at once. The logarithms do not make that argument less valid (although they are completely unnecessary here), but they also do not make the definition any more useful. —JAOTC 18:42, 12 August 2009 (UTC)
I'm not asking for you to tell me if I'm right or not, I'm asking for something to be said about it in this article. I can't see a single bit of text in it that says that 0/0 can be any number, and since the entire article is about division by zero it would make sense to mention it don’t you think? I fail to see why it isn't important and if we all went by your "if it doesn’t produce a single number it doesn’t produce any" rule then it would be impossible for a number to have a square root. Robo37 (talk) 20:50, 12 August 2009 (UTC)
Yes, you have a point here in that there are lots of useful multivalued functions, of which the complex logarithm, and therefore the unrestricted square root function, are prime examples. Many even assume an infinite number of values in each point. I still don't see the usefulness of something that simultaneously assumes all values in its codomain, though. But if you're looking to add something like "without the usual requirement that a/b be a unique number, 0/0 could instead have been defined as an entity assuming all values at once" to the article, I wouldn't be opposed to that. —JAOTC 05:36, 13 August 2009 (UTC)
Please add a citation to a journal where such a way of dealing with it is used otherwise it would be original research. Please see that link for Wikipedias policy as regards that. Dmcq (talk) 10:25, 13 August 2009 (UTC)
Something like that would be fine Jao. How is that original research? Robo37 (talk) 16:55, 13 August 2009 (UTC)
For something like this the appropriate mathematical term is 0/0 is an indeterminate form. Saying 0/0=x would be removed in a flash because it is not any sort of standard mathematical notation. You thought of it yourself and therefore it is original research in wikipedia terms. The article about original research is quite specific about this, it is one of the core policies of wikipedia. Actually I do know of a reference for stuff like this, see James Anderson (computer scientist). Really I don't advise following his path as it goes nowhere. Dmcq (talk) 17:17, 13 August 2009 (UTC)
Simply saying "0/0=x" or anything like that would be stupid, I'm asking for something like "without the usual requirement that a/b be a unique number, 0/0 could instead have been defined as an entity assuming all values at once" as Jao said above or "arguably, 0/0 can, in fact, have any number as it's answer, but representing this under a single value is where the difficulty lies”. If it’s a fact (and it seems pretty clear that it is), then why shouldn’t it be mentioned? Robo37 (talk) 17:39, 13 August 2009 (UTC)
0/0 could be defined as anything you want, even 1. The problem is that any definition would not follow the usual rules. In fact 00 is actually defined as 1 in many circumstances even though in others it is best left undefined and is also an indeterminate form. There just is no point in your definition that I can see and there isn't a literature saying that it has a point. What would be your reason for doing so? What would be the difference between what you are saying and what James Anderson (computer scientist) wrote and why would what you wrote be any better? Dmcq (talk) 20:09, 13 August 2009 (UTC)
As an aside, I think there is a basic misconception about the possibility or impossibility of dividing by zero. If someone says "we can't divide by zero", someone else will invariably hear "nobody has yet managed to divide by zero". And since it's so extremely easy to come up with a way of dividing by zero, they think they have seen something original. (I'm not saying this is what Robo37 does here, but it certainly is the way the BBC story on Anderson's nullity was worded.) The fact, as you point out and as the article maybe needs to be clearer on, is that 0/0 can be defined to be something (and that it already has been done, several times!), it just can't be defined to be something more useful than "undefined". A useful division by zero should let us, for instance, completely solve the equation x2 = x by dividing both sides by x. As far as I know, not even wheel theory accomplishes that, because it's just not accomplishable. Now, there's a gauntlet for all presumptive zero divisors (pun intended) to pick up. —JAOTC 05:14, 14 August 2009 (UTC)
There are a few bits missing, it links to defined and undefined which is a badly written article and it misses any mention of an indeterminate form in the calculus section. I think the article could be cleaned up a bit too. However it does mention that the value is not defined except in some special circumstances and it isn't too bad an article. It is also read by a lot of people, so overall there is a higher bar to aim at when editing it than many other articles, but of course anyone who's willing to put in the effort to try is welcome to give it a go. Dmcq (talk) 10:15, 14 August 2009 (UTC)
Why is there so much original research here? If you think you are correct, publish a paper, have it peer reviewed, accepted, and published in a journal, and then we can link to it. Or at least bring it up with the Math help desk. Talk pages are supposed to be for improving articles, not introducing original research. --Zarel (talk) 22:31, 14 August 2009 (UTC)
All I'm doing is suggesting an improvement to this article. Robo37 (talk) 23:00, 14 August 2009 (UTC)
As far as I recall you titled this section "0/0 = x, fact". That is not an accepted part of mathematics. Jao has tried to extract some sort of idea of what the problem is from what you said seeing that you haven't been able to read the article without difficulty. The precise ideas you have had though are simply not suitable for inclusion though and what Zarel said about them is correct. Dmcq (talk) 23:17, 14 August 2009 (UTC)
We have the No Original Research rule for a good reason - if we didn't, Wikipedia talk pages would be full of debate over whether or not your original research was correct or not. For instance, to me, it is obvious that your "fact" of "0/0 = x" is incorrect and an abuse of notation, but article talk pages are not a good place for the discussion of why. The "No original research" rule ensures that if you disagree, you take it up with professional mathematicians instead of us, and you can come back to us when professional mathematicians agree with you. --Zarel (talk) 10:51, 2 December 2009 (UTC)

Hmmm, now if you had said that 0/0 ∈ ℝ, you might have gotten some consensus. When you consider that division is the process of repeated subtraction, asking "how many times can you subtract the divisor (the denominator, here zero) from the dividend (the numerator, the other zero) before you have a remainder of or less than the divisor (zero)?" (the literal meaning of division) then clearly any real number answers correctly for the quotient, and all answers you can comprehend although indeterminate are members of ℝ. If you do the long division of 0 goes into 0, you'll see that no matter what you choose for your quotient, immediately upon back-multiplying and subtracting that product of your number from ℝ times zero, you have zero and thus are done. In that sense, your wanting to use "x" is understandable, but you need to precisely state x ∈ ℝ. (Remembering the definition of division is always helpful in resolving these issues, when you try an operation such as 1/0, you'll immediately see you'll be subtracting zero from 1 without bound, hence making it really clear why 1/0 is usually considered to be boundless and expressed 1/0 ∈ ±∞ .) —Preceding unsigned comment added by (talk) 12:59, 30 September 2010 (UTC)

zero divied by zero fallacy proof[edit]

I have one problem with that proof. 1/0 does not equal 1. 2/0 does not equal 2. They both equal infinity. So it leads to the conclusion 0/0+infinity=0/0+infinity, which explains nothing since its true. —Preceding unsigned comment added by (talk) 18:34, 18 October 2009 (UTC)

1/0 obviously doesn't equal 1, but it doesn't equal ∞ either, as that would lead to 0 × ∞ equalling 1. If there's something you don’t understand about division by zero please read the article, don't use this talk page as a forum. Robo37 (talk) 18:47, 18 October 2009 (UTC)
I was unable to find a 1/0 in the fallacy proof section never mind an assertion that it was equal to 1. You'll need to be more specific about exactly where you find a problem in an article. Dmcq (talk) 18:58, 18 October 2009 (UTC)

I would like to make known the part where the article talks about 10/0. if one were to set 10/0=x, then x times 0 would have to equal 10. the article states that x*0=0, and not 10, but if you put 10/0 in for x, you'd get (10/0)*0=10. you'd then move the 0 in the denominator, resulting in 10*(0/0)=10. now, any number divided by itself equals 1, and 0 divided by any number equals 0, so 0/0 would equal 1 or 0. this would give you 2 possibilities, the first being 10*1=10, and the second being 10*0=10. the second would obviously be extraneous, and therefore x*0=10 if x=10/0 Didlybob123 (talk) 03:08, 28 February 2013 (UTC)

Kaplan example error?[edit]

There seems to be a basic flaw in the "Fallacies based on division by zero" example.

It says

"The following must be true:

0\times 1 = 0\times 2.\,"

and then

"Dividing by zero gives:

\textstyle \frac{0}{0}\times 1 = \frac{0}{0}\times 2."

But that is NOT correct by basic algebra as you divide the entire equation by the value. So the equation should be

\textstyle \frac{0}{0}\times \frac{1}{0} = \frac{0}{0}\times \frac{2}{0}.

So either something is missing from the explanation or something else is wrong.--BruceGrubb (talk) 03:23, 1 November 2009 (UTC)

You've divided by zero twice. I'm not sure what you're up to. Perhaps you could divide the following by 5 instead of 0 in the same way just to show me what you're up to:
2 \times 3 = 6.\,
Thanks Dmcq (talk) 08:29, 1 November 2009 (UTC)
Sorry miswrote the above because I'm not used to doing formulas in wiki.
\frac{2 \times 3 = 6}{5}.\, or \frac{2 \times 3}{5} = \frac{6}{5}.\,
So the above should be
\textstyle \frac{0\times 1}{0} = \frac{0\times 2}{0}."
Yes that explains matters thanks. It should be
\frac{2}{5} \times 3 = \frac{6}{5}.\,
2 \times \frac{3}{5} = \frac{6}{5}.\,

or as you said the two multiplied together and then divided by 5.

These work out as
0.4 × 3 = 1.2 for the first one
2 × 0.6 = 1.2 for the second one
6 ÷ 5 = 1,2
Your version
\frac{2}{5} \times \frac{3}{5} = \frac{6}{5}.\,
comes out as
0.4 × 0.6 which is 0.24 whereas the right hand side is 1.2
Dividing everything on the left hand side would be correct if it was an addition or subtraction but not for a multiplication or division. For instance the following is quite correct
2 + 3 = 5 \,
\frac{2}{5} + \frac{3}{5} = \frac{5}{5} \,
or evaluating the bits
0,4 + 0.6 = 1
If you hit yourself on the forehead and say oh yes! then that's fine otherwise you'll need a bit of practice with this sort of thing to make it all clearer. The article Fraction (mathematics) goes into all this but it is an encyclopaedia article rather than a tutorial. Dmcq (talk) 23:21, 1 November 2009 (UTC)
The problem is that \frac{0}{0} is a special case as it is the one time the
if  {a \times b} = {c} then  {a} = \frac {c}{b} doesn't produce nonsense if b is 0 because any number times b equals 0. The problem is that c can be any number and you have two conflicting rules involved:
\frac{0}{b} = {0} and \frac{a}{a} = {1}
If you go with the \frac{0}{b} = {0} position then the equation makes sense again.--BruceGrubb (talk) 23:42, 1 November 2009 (UTC)

This just proves that \frac{a}{a} = {1} is wrong. Can anyone honestly tell me that \frac{0}{0} = 1? This just makes no sense. The answer could either be undefined or 0. Just think about learning devision: I have 0 objects and I put them in 0 groups. How many objects are in a (nonexistent) group? If you say 1, something is wrong with you. (talk) 20:14, 23 November 2010 (UTC)

Can anyone verify whether the "proof" is present in the Kaplan source? If it is, we don't really need the above discussion, and more importantly, we can undo this useless edit and bring the section back in line with the source. DVdm (talk) 20:29, 23 November 2010 (UTC)

In Elementary Arithmetic[edit]

Here, we mention an example of how many people satisfied with nothing can be satisfied with one apple. But this question should really be worded like this: "how many people that do not want anything can we satisfy with one apple, if it is mandatory to give everyone an apple?" In this case, each person would get an infinitely small part of the apple, so the number of people must be infinity. It is not any number - only zero over zero has an undefined, ambiguous quotient. Majopius (talk) 21:19, 16 December 2009 (UTC) contribs) 21:09, 16 December 2009 (UTC)


I think the current explanation is a bit confusing. If I may cite an "expert", this explanation by "Dr. Math" seems good. While the lim(x->0) x/x = 1, lim(x->0) 7x/x. (OR: Actually lim(x->0) ax/x = a, where a is any member of the set of complex numbers.)

Unsigned infinity[edit]

This article seems to be using the convention that ∞ and +∞ represent different concepts. This isn't wrong but it's not the only convention being used, as I mentioned recently at Wikipedia talk:WikiProject Mathematics#Unsigned infinity. There should probably be some mention in the article to specify which notation is being used to avoid confusion.--RDBury (talk) 20:13, 20 January 2010 (UTC)

Featured Page[edit]

Can this get nominated? The author of this page is a genius. It's so easy to comprehend it's ridiculous. -- (talk) 17:32, 18 February 2010 (UTC)


Should we protect this page? There has been lot's of vandalism lately. Somebody500 (talk) 00:18, 22 February 2010 (UTC)

You can file a request at WP:Requests for page protection. The current level is a bit low, so I'm not sure they will do it now. It's a very simple procedure. Go ahead and try. DVdm (talk) 08:20, 4 March 2010 (UTC)
Yes check.svg Done. I went ahead with this edit. Page is protected for two weeks. DVdm (talk) 21:49, 4 March 2010 (UTC)

removed chuck norris can divide by zero16:10, 13 May 2010 (UTC) —Preceding unsigned comment added by (talk)

Preventing linebreaks[edit]

Does anyone know how to prevent a linebreak in the middle of the expression


? I tried putting   between the a and the slash, and the slash and the zero, but it didn't work. --Trovatore (talk) 00:12, 4 March 2010 (UTC)

I have replaced it with inline math: <math>a/0</math>. DVdm (talk) 08:13, 4 March 2010 (UTC)
That's also problematic. If you force it to create a PNG, you get problems with line spacing; if you don't, the a comes out roman, which is not desired. --Trovatore (talk) 08:28, 4 March 2010 (UTC)
Hm, indeed. I undid my mod. It seems to work now. There's no linewrapping anymore from where I'm sitting. Strange. - DVdm (talk) 09:46, 4 March 2010 (UTC)

In algebra[edit]

This appears in the section "In algebra": "Although most educated people would probably recognize the above "proof" as fallacious, the same argument can be presented in a way that makes it harder to spot the error." I imagine that this is a pretty spurious claim and would be difficult to support. We should probably just remove "Although most educated people would probably recognize the above "proof" as fallacious," and the sentence will still work. Setitup (talk) 23:15, 10 March 2010 (UTC)

I agree that such a claim doesn't really belong in an encyclopedia. How's "Although it is possible to recognize the above 'proof' as fallacious,"? --Zarel (talk) 05:30, 11 March 2010 (UTC)
Even better: "Although the proof is recognizably fallacious, ..." —Anonymous DissidentTalk 06:40, 11 March 2010 (UTC)
"Recognizably" still sounds vaguely weasely. What's wrong with "Although the proof is fallacious"? --Zarel (talk) 20:53, 13 May 2010 (UTC)
Perfect. DVdm (talk) 21:14, 13 May 2010 (UTC)


The page refers to a in a/0 as a "dividend". I only heard of dividends on the stock market. Is this standard usage? Tkuvho (talk) 16:10, 1 July 2010 (UTC)

Yes, see wikt:dividend. The dividend as far as a company is concerned is the amount to be divided before it is shared out amongst the shareholders. Dmcq (talk) 18:33, 1 July 2010 (UTC)

0/0 is called "indeterminate," not "undefined."[edit]

The Math Forum at Drexel webpage has a good explanation of the difference between undefined expressions such as a/0 and indeterminate expressions such as 0/0. Indeterminate expressions could have many different answers, and it can't be "determined" which one is appropriate for a given case. Undefined expressions have no answer because the operation on the numbers is nonsensical. —Preceding unsigned comment added by (talk) 01:31, 11 August 2010 (UTC)

0/0 is one of the classic indeterminate forms, yes. But as a value it's undefined. That is, the function (technically partial function) that takes two real numbers x and y and returns x/y does not have the point (0,0) in its domain. --Trovatore (talk) 02:04, 11 August 2010 (UTC)
Almost anything can be called "undefined", as long as you don't define it (i.e. if the context is a set it's outside of). See Defined and undefined. 2−5 is undefined in the positive numbers, for instance, and 4/5 is undefined in the integers. 0/0 can be defined to be an indeterminate form. 1/0 can be defined to be an indeterminate infinity. So you could argue that they're both undefined and both indeterminate. --Zarel (talkc) 06:07, 11 August 2010 (UTC)

I agree that "0/0" is both an indetermination and undefined. But note that saying something is an indeterminate form does not define it; quite the contrary. And, unlike 2−5, which may be undefined in some mathematical structures but has a meaning in others, there is no useful mathematical structure that assigns a meaning to "0/0". FilipeS (talk) 13:15, 22 March 2012 (UTC)

Complex Infinity?[edit]

Mathematica and Wolfram Alpha (and apparently Microsoft Math) return "ComplexInfinity" when asked to evaluate 1/0.

Wolfram MathWorld mentions them here:

I think it deserves more of a mention than in the "in computer arithmetic" section. To me, "in computer arithmetic" should talk about how computers handle problems they're not intended to be able to solve. On the other hand, Mathematica is, as far as I know, returning what Wolfram Research believes to be the correct answer.

Thoughts? --Zarel (talkc) 02:40, 12 August 2010 (UTC)

It's in the "Riemann sphere" section. --Trovatore (talk) 02:42, 12 August 2010 (UTC)
Not entirely. The MathWorld "Complex Infinity" article describes it as a number in the complex plane, not a Riemann sphere, and the words "complex infinity" are not used in the Riemann sphere section of our article. --Zarel (talkc) 03:13, 12 August 2010 (UTC)
OK, here's a tip — never rely on MathWorld for terminology. It's math is usually right as far as I can tell, but sometimes it just makes up words more or less.
As far as the substance goes, no, it is not a number in the complex plane. By definition the complex plane is a plane; it has no point at infinity. When you add the point at infinity you don't have a plane anymore; you have a sphere. --Trovatore (talk) 04:41, 12 August 2010 (UTC)

question about internet culture popularity[edit]

Should we make a reference to dividing by zero becomeing an internet meme as it is quite popular among message boards in demotavationals? --anon

We wait till things appear in WP:Reliable sources. It just needs an newspaper column for instance to mention its use on the web. Dmcq (talk) 08:50, 21 March 2011 (UTC)

What about Chuck?[edit]

Everyone knows that Chuck Norris candivide by zero? —Preceding unsigned comment added by (talk) 23:43, 6 May 2011 (UTC)

He also served in the United States Air Force, that doesn't mean the article on the United States Air Force need mention him. One would only be interested in that if one was going to read about Chuuck Norris anyway, It has zilch interest of a reader just reading this article. Dmcq (talk) 10:01, 7 May 2011 (UTC)

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The Word Problem is Not Helpful[edit]

They (you know who they are, don't you?) always phrase the word problem something like this: "So for dividing by zero – what is the number of apples that each person receives when 10 apples are evenly distributed amongst 0 people?"

But I prefer to phrase it like this: "Given 10 apples, how many piles of apples can you make if you put 0 apples in each pile?" (or, to keep it in terms of people instead of piles: "Given 10 apples, how many people can you give an apple to if you give 0 apples to each person?)

Clearly, here, the answer is an infinite number of piles or people.

I've been "trained" in all the right stuff, and believe that for the good of mathematicians everywhere, division by 0 must be undefined. I've even seen what I believe is the deep seated reason behind it (which I didn't look for in the article, and have to admit I didn't even read the entire article).

It's just that I think using that word problem as an example of why division by zero is undefined is not useful, and, in fact, counterproductive. With some thought, people (perhaps like me) can look at it the way I do, and realize that the word problem is just a sham--it does not do anything to prove that division by zero is undefined.

If you want to educate people, or be an encyclopedia, provide the real explanation. Rhkramer (talk) 00:27, 15 June 2011 (UTC)

If you put no apples into each pile, then they are not piles of apples. They are piles of air. You do not end up with infinite piles of apples. Your question is undefined. Fred775 (talk) 01:25, 12 January 2015 (UTC)

Pop Culture[edit]

There ought to be a section explaining the cultural impact made by the idea of division by zero. This is evident whenever one searches divide by zero, a series of playful images result showing how the modern culture has made somewhat of a "play" on the idea. — Preceding unsigned comment added by Ghost9420 (talkcontribs) 15:16, 16 June 2011 (UTC)

If you can find a WP:reliable source that discusses this then that could form the basis for such section. I've seen sources discussing all sorts of things so somebody may have thought of something like this. Without that it would really have to be something that actually used the concept in some meaningful way and was noted by someone, see WP:TRIVIA and WP:handling trivia. Dmcq (talk) 15:25, 16 June 2011 (UTC)

File:MS cal divide by zero.png Nominated for speedy Deletion[edit]

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Mahavira, and the number remaining unchanged[edit]

To divide zero times is to not divide. So to divide 7 by zero would be not to divide it, and let it remain 7. Because zero is the subject not an object (if zero were an object it would be one as a subject, but that's a philosophic question and not a mathematical). Now dividing "zero" seven times is another issue, because such an operation posits zero as an object by definition. Mathematics should do well to consider numbers as objects or subjects. For example, 1 as an object is singular even amidst multiplicity, 1 as a subject is unity or the whole considered at the whole without multiplicity. Nagelfar (talk) 02:12, 14 September 2011 (UTC)

Why did you write that? In what way are you hoping to improve the article? Dmcq (talk) 02:29, 14 September 2011 (UTC)
Maieutic improvement through dialectical discussion. For example, why should dividing by zero be undefined, but subtracting 50% from zero is still zero? Shouldn't it be -50% of undefined? I wouldn't add to article to of course avoid original research, but posting here as looking to those who may know sources of opinions of mathematicians based on notoriety of said opinions for improvement of said article. Nagelfar (talk) 04:09, 14 September 2011 (UTC)
If you want a discussion about things rather than improving the article then Wikipedia:Reference desk/Mathematics would be better though it really is just for answering questions. There are no forums as such on WIkipedia. I can say though the whole basis of the way you're going about it strikes no chord with modern mathematics. Discussion of an individual instance of division and trying to give a value on its own would normally be seen as a fruitless idea. What is wanted is general ideas so one wants a general definition of division and have the result come out of that. And the general idea of division is that it is an inverse operation to multiplication. The result of a/b is c if c is the unique value such that a×c is b. If there is no such value one might be able to extend the system as described for the projective real line in the article where ≈ is used - but then one has problems with comparisons as it may be positive or negative and 0/0 still isn't defined and there's no good reason to define it as a particular value when any value can satisfy 0×c=0. Dmcq (talk) 09:00, 14 September 2011 (UTC)
"What is wanted is general ideas so one wants a general definition of division and have the result come out of that. <...> and 0/0 still isn't defined and there's no good reason to define it as a particular value <...>" Why not explain it in the article? The tradition is to put in separate places statements and explanations, but this clearly doesn't work well for an encyclopedia article. For example, purposes of defining things are to be explained in-place, so that possible and quite logical misconceptions be ruled out immediately; this is more reader-friendly. I'd do the work myself, but I'm afraid to go too far from sources or make a mess with my English, so I'm out. - (talk) 15:15, 7 April 2013 (UTC)

Sanskrit mathematics & Division by zero as infinity[edit]

According to "The Universal History of Number" by Georges Ifrah, page 476: "Khahâra. Sanskrit word for infinity. Literally "division by zero". Notably used by *Bhâskarâchârya. See Khachheda. ... Khachheda. Sanskrit term used to denote infinity. Literally "divided by zero" (from *kha, "space" as a symbol for zero, and chheda, "the act of breaking into many parts", "division"). Thus it is the quantity whose denominator is zero". The term is used notably in this sense by *Brahmagupta in his Brahmasphutasiddânta (628 CE)." Nagelfar (talk) 00:24, 19 September 2011 (UTC)

That's already in the article in the section 'Early attempts' Dmcq (talk) 07:55, 19 September 2011 (UTC)
No it's not. There's no mention of Bhâskarâchârya whatsoever, nor does it say it is equated with infinity, but rather zero. Nagelfar (talk) 03:55, 20 September 2011 (UTC)
From that section: "Bhaskara II (1114–1185) tried to solve the problem by defining (in modern notation) \textstyle\frac{n}{0}=\infty.[1] This definition makes some sense, as discussed below, but can lead to paradoxes if not treated carefully. These paradoxes were not treated until modern times." Dmcq (talk) 07:53, 20 September 2011 (UTC)
Yes I read that, this post was in response to that very section obviously. It neglects to say the same of Brahmagupta's interpretation (it says zero). There's no mention whatsoever of Khahâra. Nagelfar (talk) 13:37, 21 September 2011 (UTC)
You should have said what you meant. This is the English wikipedia, why should it stick in Indian words rather than just say infinity? Is there something of note about that word in this context? That section does talk about Brahmaguptra and you haven't said anything extra that's not there, so how should more be put in? Are you saying that the text is wrong about what he said or something? Please be clear in exactly what you are saying should be there. Dmcq (talk) 15:20, 21 September 2011 (UTC)
Let me stop my same quotation before the ellipses "According to "The Universal History of Number" by Georges Ifrah, page 476: "Khahâra. Sanskrit word for infinity. Literally "division by zero". Notably used by *Bhâskarâchârya. See Khachheda." now, all that information is new. I'm sorry my second quotation from that work was distracting. The point is, the word used for infinity (Khahâra) meant "division by zero" literally, now I'd say that is notable for any language, and it was used by Bhâskarâchârya, one not mentioned in the article. The article says Brahmaguptra claimed that division by zero equals zero, my quotation for Brahmaguptra says he used it as infinity, that is something from my second quotation that is "not there". Is that clearer? It's nothing that wasn't in my first posting. Nagelfar (talk) 20:04, 21 September 2011 (UTC)
Bhaskara II is Bhâskarâchârya. Zero divided by zero was zero according to Brahmaguptra, not just any division by zero. He represented a number other than zero divided by zero by the number over zero, he did not say it was a particular value but he did make a mess of things saying for instance that 5/0 × 0 was 5. You don't get that by replacing 5/0 by infinity, he did not change 5/0 into something else. Dmcq (talk) 21:28, 21 September 2011 (UTC)
In the very least, I think that there being words for infinity in Sanskrit which mean literally "division by zero" is of note to the history portion. Nagelfar (talk) 22:37, 21 September 2011 (UTC)
The Sanskrit for infinity is ananta for without end. People later on interpreted n/0 as infinity but he didn't call it infinity, he called it divided by zero which is exactly what it is. Dmcq (talk) 11:25, 23 September 2011 (UTC)

The simple parts.[edit]

The division being undefined because of the multiplication doesn't make sense. A number times zero should equal the number, n x 0 = n. N is a number which represents real value. So if I have 8 Coke bottles and I multiply them zero times, the 8 Cokes do not magically disappear, they are still there. In reverse of that, a number divided by zero would be would also equal the number n/0 = n. — Preceding unsigned comment added by Gummifaustus (talkcontribs) 00:45, 19 September 2011 (UTC)

n x 0 = n and n x 1 = n would give n x 1 − n x 0 = 0 or n x (1 − 0) = 0 which is n x 1 = 0. Nothing magical happens when you multiply. If you get no deliveries of a six pack of coke you don't have any coke. If you get one delivery of a six pack of coke you have a six pack of coke. Dmcq (talk) 08:01, 19 September 2011 (UTC)


If dividing by 0 was possible,then there could be 2 numbers:x and y to satisfy x/y (or y/x)=0 Since I don't know any numbers which fulfill this,then dividing by 0 is impossible.Oh,and x and y are not 0 — Preceding unsigned comment added by (talk) 16:14, 21 May 2012 (UTC)

I am not sure why you stuck this here. This page is about improving the article and we cannot use people's own arguments, the stuff has to be from books or papers or a very reliable web source. As to the argument itself no reason was given for the conditions and your not being able to think of some numbers doesn't constitute a proof. Dmcq (talk) 09:05, 23 May 2012 (UTC)

Zero divided by zero[edit]

Any number times zero equals zero,so zero divided by zero equals any number you want — Preceding unsigned comment added by (talk) 18:14, 12 June 2012 (UTC)

That's why this thing is said to be undefined. The symbol 0/0 has no meaning. See the article. - DVdm (talk) 18:57, 12 June 2012 (UTC)
I think the article probably should have a separate section about 0/0 as it has a special status as an indeterminate and has been discussed in detail itself. Dmcq (talk) 09:25, 28 July 2012 (UTC)

Creative Numbers...[edit]

Creative numbers have purported to solve the problem of division by zero. I'm no mathematician but perhaps someone who understands the subject matter more critically could check out and see if it warrants expanding the article. (talk) 18:22, 4 January 2013 (UTC)

Its original research, with no rigorous proof or peer review. It doesn't merit inclusion here. Mindmatrix 18:40, 4 January 2013 (UTC)
I guess you would know better than I would. But, it makes sense to me as a layman. (talk) 19:31, 4 January 2013 (UTC)

1/0 > Infinity[edit]

I read all explanations in this article, but I am not sure if this was mentioned. The logic is simple. If we devide a number (let's say 1) by an infinitesimal number, we'll have an infinity as result. The zero is still smaller than the infinitesimal number so deviding a number (1 in our case) by zero, will result as a bigger number than infinity. But this is absurd since by deffinition there is nothing bigger than infinity. So division by zero is impossible. Such a number can not exist (neither exist the zero by the way, but we have some abstract understanding for it as an absence of something). — Preceding unsigned comment added by Stan3u (talkcontribs) 22:32, 11 February 2013 (UTC)

The cases where the subject matter of the article makes sense should be treated prominently in the lead[edit]

For some time, I'm not sure how long, you've been able to read the lead section without any explicit mention of the fact that division by zero (note that this is the title of the article, therefore what the article is supposed to be about) actually sometimes does make sense.

MvH's recent edit (this one) removed the only obscure allusion to that fact in the lead. I don't think that's the right way to go. There needs to be an explicit mention, not in a note but in visible text. I am not claiming my text is necessarily the optimal way of achieving that; any suggestions for making it less technical are welcomed. --Trovatore (talk) 22:31, 4 March 2014 (UTC)

Calculator image[edit]

Do we really need two calculator division-by-zero screenshots, one saying "ERROR 02 DIV BY ZERO" and the other saying "\infty"? I assume - the latter being an Android calculator on a phone - they're functionally identical and that you can't perform further operations on the infinity value. --McGeddon (talk) 17:36, 6 June 2014 (UTC)

You may be right that they are functionally identical.
But they look very different.
In systems that use IEEE floating point, you *can* perform further operations on the infinity value (sometimes spelled "Number.POSITIVE_INFINITY", "+inf", etc.). --DavidCary (talk) 19:10, 15 November 2014 (UTC)