Integers under Multiplication form Countably Infinite Commutative Monoid

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Theorem

The set of integers under multiplication $\left({\Z, \times}\right)$ is a countably infinite commutative monoid.

Proof

First we note that Integers under Multiplication form Monoid.

$\Box$

Then we have:

Commutativity

$\Box$

Infinite

$\blacksquare$