Integers under Multiplication form Countably Infinite Commutative Monoid

Theorem
The set of integers under multiplication $\struct {\Z, \times}$ is a countably infinite commutative monoid.

Proof
First we note that Integers under Multiplication form Monoid.

Then we have:

Commutativity
Integer Multiplication is Commutative.

Infinite
Integers are Countably Infinite.