Rational Numbers form Field

Theorem
Consider the algebraic structure $\left({\Q, +, \times}\right)$, where:


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

Then $\left({\Q, +, \times}\right)$ forms a field.

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