Integers under Multiplication form Countably Infinite Semigroup
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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.
$\blacksquare$