Algebraic number
High school
A number $a$ is an algebraic number if $a$ is a solution to a polynomial equation whose coefficients are all integers.
Undergraduate
Consider a real or complex number $a$. The number $a$ is an algebraic number if $a$ is a root of a nonzero polynomial with integer coefficients.
Examples
Examples
-
$\sqrt{2}$
High school
$\sqrt{2}$ is an algebraic number, because it solves $x^2 = 2$, or equivalently, it is a root of $x^2 - 2$.
Non-examples
Things that may be mistaken for examples.
- $\pi$ Elementary