Integers under Multiplication form Countably Infinite Semigroup

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

Closure
Integer Multiplication is Closed.

Associativity
Integer Multiplication is Associative.

Infinite
Integers are Countably Infinite.

The criteria for $\left({\Z, \times}\right)$ to be a countably infinite semigroup are seen to be satisfied.