Can't Mod Zero?

The C++ Standard(2003) says in §5.6/4,

[...] If the second operand of / or % is zero the behavior is undefined; [...]

That is, following expressions invoke undefined-behavior(UB):

X / 0; //UB
X % 0; //UB

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Note also that -5 % 2 is NOT equal to -(5 % 2) (as Petar seems to suggest in his comment to his answer). It's implementation-defined. The spec says (§5.6/4),

[...] If both operands are nonnegative then the remainder is nonnegative; if not, the sign of the remainder is implementation-defined.

This answer is not for the mathematician. This answer attempts to give motivation (at the cost of mathematical precision).

Mathematicians: See here.

Programmers: Remember that division by 0 is undefined. Therefore, mod, which relies on division, is also undefined.

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This represents division for positive X and D; it's made up of the integral part and fractional part:

(X / D) =   integer    +  fraction
        = floor(X / D) + (X % D) / D

Rearranging, you get:

(X % D) = D * (X / D) - D * floor(X / D)

Substituting 0 for D:

(X % 0) = 0 * (X / 0) - 0 * floor(X / 0)

Since division by 0 is undefined:

(X % 0) = 0 * undefined - 0 * floor(undefined)
        = undefined - undefined
        = undefined

X % D is by definition a number 0 <= R < D, such that there exists Q so that

X = D*Q + R

So if D = 0, no such number can exists (because 0 <= R < 0)