Rational Numbers under Multiplication form Commutative Monoid

Theorem
The set of rational numbers under multiplication $\struct {\Q, \times}$ forms a countably infinite commutative monoid.

Proof
From Rational Numbers under Multiplication form Monoid, $\struct {\Q, \times}$ is a monoid.

Then we have:

Commutativity
Rational Multiplication is Commutative.

Infinite
Rational Numbers are Countably Infinite.