Rational Numbers form Field

Theorem
Consider the algebraic structure $\struct {\Q, +, \times}$, where:


 * $\Q$ is the set of all rational numbers
 * $+$ is the operation of rational addition
 * $\times$ is the operation of rational multiplication.

Then $\struct {\Q, +, \times}$ forms a field.

Proof
This is demonstrated in the formal definition of rational numbers.