Integers under Multiplication form Countably Infinite Commutative Monoid

Theorem
Let $$\mathbb{Z}$$ be the set of integers.

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

Closure
Integer Multiplication is Closed.

Associativity
Integer Multiplication is Associative.

Identity
Integer Multiplication Identity is $\left[\!\left[{1, 0}\right]\!\right]_\boxminus$.

Infinite
Integers are Infinite.