Definition:Algebraic Number

Definition

The set of algebraic numbers $\Bbb A$ is the subset of the complex 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 $\Q$, since these are roots of linear polynomials.
• $\sqrt 2$, since it is a root of $x^2 - 2$.
• The golden section $\varphi$, since it is a root of $x^2 - x - 1$.
• The complex number $0 + i$, since it is a root of $x^2 + 1$.

Also see

• Results about algebraic numbers can be found here.

Sources

• Steven A. Gaal: Point Set Topology (1964)... (previous)... (next): Introduction to Set Theory: $2$. Set Theoretical Equivalence and Denumerability