Integers under Multiplication form Countably Infinite Commutative Monoid

Theorem
Let $$\Z$$ be the set of integers.

The structure $$\left({\Z, \times}\right)$$ is a countably infinite commutative monoid.

Closure
Integer Multiplication is Closed.

Associativity
Integer Multiplication is Associative.

Identity
Integer Multiplication Identity is $1$.

Infinite
Integers are Countably Infinite.