Rational Numbers form Field

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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.

$\blacksquare$


Sources