Rational Addition is Associative

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

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

So $\struct {\Q, +, \times}$ is a field, and therefore a priori $+$ is associative on $\Q$.