Algebraic numbers

Algebraic Numbers, are real numbers which are roots of some finite degree polynomial with integer coefficients. Examples of Algebraic Numbers are $2$, $1/3$, and ${\sqrt {2}}$.

In contrast, Transcendental Numbers are real numbers which are not roots of any finite degree polynomial with integer coefficients. The most well-known transcendental numbers are $e$ and $\pi$.

The set of Algebraic Numbers is countably infinite. This follows from the fact that the set of finite degree polynomials with integer coefficients is countably infinite.