Why is n mod 0 undefined? I tried to find out what $n$ mod $0$ is, for some $n\in \mathbb{Z}$. Apparently it is an undefined operation - why?

In general, $x = n \pmod a$ is defined by letting $x$ be the remainder of $n$ upon division by $a$. But division by zero isn't well-defined.

Added from comment: As mixedmath points out, the use of the idea of "modulo" has a higher definition as a group theoretic concept in which regarding numbers $\pmod{n}$ is equivalent to considering cosets $n\Bbb{Z}$ in the group of integers and forming the quotient group $\Bbb{Z}/n\Bbb{Z} = \Bbb{Z}_n$. But then taking $n = 0$ doesn't really tell you anything, since the quotient group is just $\Bbb{Z} / 0 \cong \Bbb{Z}$.
