Rational Numbers form Subfield of Real Numbers

Theorem
The field $$\left({\Q, +, \times; \le}\right)$$ of rational numbers forms a subfield of the field $$\left({\R, +, \times; \le}\right)$$ of real numbers.

That is, the totally ordered field of real numbers $$\left({\R, +, \times; \le}\right)$$ is an extension of the rational numbers $$\left({\Q, +, \times; \le}\right)$$.