Non-Zero Integer has Finite Number of Divisors

Theorem

Let $n \in \Z_{\ne 0}$ be a non-zero integer.

Then $n$ has a finite number of divisors.

Proof

Let $S$ be the set of all divisors of $n$.

$\forall m \in S: -n \le m \le n$

Thus $S$ is finite.

$\blacksquare$