Transcendental number
High school
A transcendental number is a number that does not solve any polynomial equation with integer coefficients.
Undergraduate
A transcendental number is a (real or complex) number that is not algebraic.
Examples
Examples
-
$\pi$
Elementary
$\pi$ is transcendental: Lindemann proved in 1882 that $\pi$ is not a root of any nonzero polynomial with integer coefficients.
- $e$ High school
Non-examples
Things that may be mistaken for examples.
- $\sqrt{2}$ High school