Rational Addition is Associative

Theorem
The operation of addition on the set of rational numbers $\Q$ is associative:
 * $\forall x, y, z \in \Q: x + \left({y + z}\right) = \left({x + y}\right) + z$

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 $+$ is associative on $\Q$.