Definition:Algebraic Number

Definition
The set of algebraic numbers $\Bbb A$ is the subset of the real numbers which are roots of polynomials with rational coefficients.

It can be seen that this definition of algebraic is consistent with the definition of algebraic over the field of rational numbers.

The algebraic numbers include:
 * The elements of the set of rational numbers $\Q$
 * $\sqrt 2$
 * The golden section $\varphi$.