Rational Numbers under Multiplication form Commutative Monoid

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

Proof
From Rational Numbers under Multiplication form Monoid, $\left({\Q, \times}\right)$ is a monoid.

Then we have:

Commutativity
Rational Multiplication is Commutative.

Infinite
Rational Numbers are Countably Infinite.