Integers under Multiplication form Countably Infinite Semigroup

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Theorem

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


Proof

From Integers under Multiplication form Semigroup, $\left({\Z, \times}\right)$ is a countably infinite semigroup.

Then we have that the Integers are Countably Infinite.

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

$\blacksquare$