# Zero divided by zero **URL:** \ **Category:** Factual Questions\ **Created:** [October 4, 2004, 8:02pm UTC](https://boards.straightdope.com/t/zero-divided-by-zero/267516 "2004-10-04T20:02:51Z")\ **Posts on this page:** 12\ **Page:** 4
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [October 6, 2004, 12:46pm UTC](https://boards.straightdope.com/t/zero-divided-by-zero/267516/61 "2004-10-06T12:46:42Z")
> [@Colophon](#): > > Ah, but what do you get if you add 0.999… to 0/0? Go cut me a switch, boy, and I’ll show ya what ya get… ---
**Author:** ![Excalibre](https://avatars.discourse-cdn.com/v4/letter/e/898d66/32.png) [@Excalibre](https://boards.straightdope.com/u/Excalibre)\ **Post date:** [October 6, 2004, 12:59pm UTC](https://boards.straightdope.com/t/zero-divided-by-zero/267516/62 "2004-10-06T12:59:54Z")
> [@Mathochist](#): > > There are right and wrong answers, and within a culture socially driven by soft and squishy academic disciplines with no right or wrong answers this can be off-putting at first. Which disciplines are those? Because I think I’d like to change my field of study . . . ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [October 6, 2004, 1:10pm UTC](https://boards.straightdope.com/t/zero-divided-by-zero/267516/63 "2004-10-06T13:10:10Z")
> [@Excalibre](#): > > Which disciplines are those? Because I think I’d like to change my field of study . . . English, philosophy, history, sociology, the whole slew of spinoffs of history and sociology called “\ studies”, political science, the more political end of economics, psychology… Actually, even though there _are_ right and wrong answers in most hard sciences, in practice it often doesn’t matter because if you lay your emphasis more squarely on the experimental end than the theoretical end it doesn’t matter. Formulate a hypothesis, test it, prove it wrong, publish. If I could publish results nobody had ever before proven _wrong_, I’d have had tenure _years_ ago. ---
**Author:** ![Canadjun](https://avatars.discourse-cdn.com/v4/letter/c/76d3ee/32.png) [@Canadjun](https://boards.straightdope.com/u/Canadjun)\ **Post date:** [October 6, 2004, 1:13pm UTC](https://boards.straightdope.com/t/zero-divided-by-zero/267516/64 "2004-10-06T13:13:02Z")
> [@bot0004](#): > > if 0/0 was equal to 0 then 6(0/0)=3(0/0), 0=0 would be correct, or? No, because if 0/0 was equal to anything including 0, I could still cancel it from both sides of your equation to make 6=3. In case you object that I’m not allowed to cancel zeroes in 6_0=3_0 it is exactly because 0/0 is undefined (to cancel the zeroes I’d have to divide both sides by 0). ---
**Author:** ![nivlac](https://avatars.discourse-cdn.com/v4/letter/n/3bc359/32.png) [@nivlac](https://boards.straightdope.com/u/nivlac)\ **Post date:** [October 6, 2004, 4:12pm UTC](https://boards.straightdope.com/t/zero-divided-by-zero/267516/65 "2004-10-06T16:12:12Z")
Precisely. As I previously posted, if 0/0 is defined to be any number, then you can show any number is equal to any other number. Can’t have that. So 0/0 is undefined. That’s the easiest explanation without getting into rings, fields, etc. ---
**Author:** ![bot0004](https://avatars.discourse-cdn.com/v4/letter/b/858c86/32.png) [@bot0004](https://boards.straightdope.com/u/bot0004)\ **Post date:** [October 6, 2004, 5:22pm UTC](https://boards.straightdope.com/t/zero-divided-by-zero/267516/66 "2004-10-06T17:22:41Z")
I think nivlac is correct, but to address dmartin, if you cancel the 0/0 from both sides, you’d simply get 0 again, and hence be stuck in an infinate loop, right? Also, nivlac, since we can take that answer to point, what do you mean by "getting into rings, fields, etc. I’d like to know, so if you, or anyone else, don’t mind explaining this to me, be very nice. ---
**Author:** ![bot0004](https://avatars.discourse-cdn.com/v4/letter/b/858c86/32.png) [@bot0004](https://boards.straightdope.com/u/bot0004)\ **Post date:** [October 6, 2004, 5:33pm UTC](https://boards.straightdope.com/t/zero-divided-by-zero/267516/67 "2004-10-06T17:33:24Z")
WAIT! You can’t just say 6(0/0) = 3(0/0), if you do: 6x=3x 3x=0 x=0 then it seems to be ok…i mean consider this 6(2/2)=3(2/2) 6=3 obviously thats wrong, so you need to use variables first and foremost, before stating that if 0/0 equaled 1 or 0. IF that were true, you could use any number over itself to prove 6=3. HOWEVER, (6x/0) = (3x/0) for x=0 (assume 0/0 equals 1) (6_0/0) = (3_0/0) 6=3 [obviously this is wrong] now let’s try another situation, (6x/0) = (3x/0) for x=0 (assume 0/0 equals 0) (6_0/0) = (3_0/0) 0=0 [true!] rebuttals anyone? ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [October 6, 2004, 5:34pm UTC](https://boards.straightdope.com/t/zero-divided-by-zero/267516/68 "2004-10-06T17:34:56Z")
> [@bot0004](#): > > rebuttals anyone? It’s the old truth–if you assume something false (0/0 = 1 in your case), you can prove any damn thing you like. That doesn’t mean what you’ve proved is true. ---
**Author:** ![Enola\_Straight](https://avatars.discourse-cdn.com/v4/letter/e/dec6dc/32.png) [@Enola\_Straight](https://boards.straightdope.com/u/Enola_Straight)\ **Post date:** [October 6, 2004, 6:18pm UTC](https://boards.straightdope.com/t/zero-divided-by-zero/267516/69 "2004-10-06T18:18:12Z")
X/X=1 0/X=0 X/0=infinity I say 0/0= all numbers from negative infinity to positive infinity, inclusive. I say. 😉 ---
**Author:** ![Complex\_Conjugate](https://avatars.discourse-cdn.com/v4/letter/c/3bc359/32.png) [@Complex\_Conjugate](https://boards.straightdope.com/u/Complex_Conjugate)\ **Post date:** [October 6, 2004, 6:18pm UTC](https://boards.straightdope.com/t/zero-divided-by-zero/267516/70 "2004-10-06T18:18:37Z")
> [@bot0004](#): > > Also, nivlac, since we can take that answer to point, what do you mean by "getting into rings, fields, etc. I’d like to know, so if you, or anyone else, don’t mind explaining this to me, be very nice. If you read the rest of the therad you will see what is meant by this. To a mathematicvan ‘0’ is a generic term for the additve identity so we can only examine the quetsion by looking at general classes of objects that have an additive identity and some way of defining divison - a ring is probably the most general class of objet that has this, a field is a specifc type of ring (the integers are a ring, but not a field, whereas the rationals, the reals, the complex numbers are all fields). The problem is that unless you say what your talking about (i.e. the rationals, reals, etc.) then we can only assume the most general case. Those who did not try to adress it terms of rings, etc, didn’t even say which matahematical object they were talking about; if you don’t specify what your talking about it’s impossible to prove anything. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [October 6, 2004, 6:58pm UTC](https://boards.straightdope.com/t/zero-divided-by-zero/267516/71 "2004-10-06T18:58:46Z")
> [@ultrafilter](#): > > It’s the old truth–if you assume something false (0/0 = 1 in your case), you can prove any damn thing you like. That doesn’t mean what you’ve proved is true. 2+2 = 5 implies 1 = 2 implies two are one. The Pope and I are two, hence the Pope and I are one, hence I am the Pope. – Russell ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [October 6, 2004, 7:01pm UTC](https://boards.straightdope.com/t/zero-divided-by-zero/267516/72 "2004-10-06T19:01:27Z")
> [@Complex Conjugate](#): > > The problem is that unless you say what your talking about (i.e. the rationals, reals, etc.) then we can only assume the most general case. Those who did not try to adress it terms of rings, etc, didn’t even say which matahematical object they were talking about; if you don’t specify what your talking about it’s impossible to prove anything. Well, those who didn’t say rings generally quoted what they remember from calculus: “0/0 is indeterminate”, which is really shorthand (they’d forgotten) for “0/0 is an indeterminate form of a limit”. A perfectly understandable mistake, though a mistake nonetheless. [Previous page](https://boards.straightdope.com/t/zero-divided-by-zero/267516.md?page=3)