# transcendental number

A transcendental number is a complex number that is not an algebraic number. That is, it is a complex number that is transcendental over $\mathbb{Q}$ (or, equivalently, over $\mathbb{Z}$).

Well known transcendental numbers include $\pi$ and $e$ (the base of natural logarithms).

Cantor showed that, in a sense, “almost all” complex numbers are transcendental: there are uncountably many complex numbers, but only countably many algebraic numbers (http://planetmath.org/AlgebraicNumbersAreCountable).

Title transcendental number TranscendentalNumber 2013-03-22 11:55:54 2013-03-22 11:55:54 yark (2760) yark (2760) 13 yark (2760) Definition msc 11J82 msc 11J81 Pi Irrational