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
Canonical name	TranscendentalNumber
Date of creation	2013-03-22 11:55:54
Last modified on	2013-03-22 11:55:54
Owner	yark (2760)
Last modified by	yark (2760)
Numerical id	13
Author	yark (2760)
Entry type	Definition
Classification	msc 11J82
Classification	msc 11J81
Related topic	Pi
Related topic	Irrational