Rational Multiplication is Associative

Theorem
The operation of multiplication on the set of rational numbers $$\Q$$ is associative:


 * $$\forall x, y, z \in \Q: x \times \left({y \times z}\right) = \left({x \times y}\right) \times z$$

Proof
Follows directly from the definition of rational numbers as the quotient field of the integral domain $$\left({\Z, +, \times}\right)$$ of integers.

So $$\left({\Q, +, \times}\right)$$ is a field, and therefore a priori $$\times$$ is associative on $$\Q$$.