Why is 0 mod 0 an error?

Question

If I type:

int main() { return 0 % 0; }

I get back an error:

error C2124: divide or mod by zero

What is the reason behind this? Isn't the answer zero?

@0x499602D2: Well, division is undefined because 0 × N = 0 has an infinite number of solutions for N. But doesn't 0 × N + M = 0 has only *one* solution for M, which is zero, don't you agree? — user541686, Oct 15 '13 at 00:21
I do agree, but I'm not sure I understand the specifics for why this particular expression is undefined. — David G, Oct 15 '13 at 00:23
Isn't this is more of a math question rather than a programming one? — user2802841, Oct 15 '13 at 00:23
@user2802841: I'm not sure, is it generally undefined in math too? I only came across it when my code crashed, I don't remember ever having seen this in any math book before. — user541686, Oct 15 '13 at 00:24
Modulo is the remainder of the division, simple as that. If no division is possible, the modulo isn't either. Your pseudo alternative to the modulo function doesn't apply to what actually happens. — Havenard, Oct 15 '13 at 00:24
@Havenard: With regard to unsigned integers, defining `x%0 == 0` would constitute an exception to the principle that `x%y < y`. With regard to floating-point values, I think `fmod(x,0)` should have been defined as zero, given that, mathematically speaking, for any x, the limit as (y->0) of fmod(x,y) is zero. — supercat, Oct 30 '13 at 22:34
Besides, although `0/0` is undefined because there is no unique value `x` for which `0*x==0`, there is exactly one possible value of y such that `0*x+y == 0`. — supercat, Oct 30 '13 at 22:42
Not sure what you're saying but a modulo returning 0 means the remainder of the division is 0. Its impossible to affirm that the remainder of a division by 0 is 0 if a division by 0 is mathematically undefined to begin with. I understand for some applications it is convenient to think that the result of a modulo, or even a division by 0, is 0, but that is not correct. — Havenard, Oct 30 '13 at 22:47
Possible duplicate of [How to divide by zero without error](http://stackoverflow.com/questions/17001417/how-to-divide-by-zero-without-error) — Gnemlock, Jan 20 '17 at 07:02
For reference regarding the mathematics behind the operation: https://math.stackexchange.com/questions/516251/why-is-n-mod-0-undefined — Andrew, Oct 04 '17 at 21:44

score 13 · Accepted Answer · answered Oct 15 '13 at 00:19

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In mathematics, x mod 0 is undefined, hence the error.

answered Oct 15 '13 at 00:19

David G

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Okay I admit I didn't know that. (I'd never even thought about it before.) Guess I'll go ask on Math.SE... thanks. – user541686 Oct 15 '13 at 00:26
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0x499602D2, you are too categorical. One convention is that x (mod 0) is x. The rationale is as follows: In modular arithmetic, z ≡ x (mod y) means that there is some integer k such that z - x = k * y. If y = 0, then we get z - x = 0 or z = x. – Peter John Acklam Apr 03 '15 at 18:56

score 5 · Answer 2 · answered Oct 15 '13 at 00:30

From C++ standard, section 5.5:

If during the evaluation of an expression the result is not mathematically defined or not in the range of representable mathematical values for its type, the behavior is undefined. [...] Treatment of division by zero, forming a remainder using a zero divider, and all floating point exceptions vary among machines, and is usually adjustable by a library function.

Since remainder of a division by zero is mathematically undefined regardless of the number being divided, the answer is undefined according to the C++ standard.

score 1 · Answer 3 · answered Oct 15 '13 at 00:19

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The mod function is effectively the same as the integer division function, except that it gives you the remainder, rather than the quotient. You can't divide by zero...

(BTW, as an aside, 0/0 is not even infinity, it's indeterminate.)

answered Oct 15 '13 at 00:19

jwismar

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Why is 0 mod 0 an error?

3 Answers3

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