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 $$\Q$$.