# Integers under Multiplication form Countably Infinite Semigroup

## Theorem

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

## Proof

From Integers under Multiplication form Semigroup, $\struct {\Z, \times}$ is a countably infinite semigroup.

Then we have that the Integers are Countably Infinite.

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

$\blacksquare$