Non-Zero Integer has Finite Number of Divisors
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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 $n$.
Then from Absolute Value of Integer is not less than Divisors:
- $\forall m \in S: -n \le m \le n$
Thus $S$ is finite.
$\blacksquare$