Rational Addition is Commutative

From ProofWiki
Jump to navigation Jump to search


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

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


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

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