Rational Addition is Commutative

Theorem
The operation of addition on the set of rational numbers $\Q$ is commutative:


 * $\forall x, y \in \Q: x + y = y + x$

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 commutative on $\Q$.