transcendental number

A transcendental numberMathworldPlanetmath is a complex numberPlanetmathPlanetmath that is not an algebraic numberMathworldPlanetmath. That is, it is a complex number that is transcendental over (or, equivalently, over ).

Well known transcendental numbers include π and e (the base of natural logarithmsMathworldPlanetmathPlanetmathPlanetmath).

Cantor showed that, in a sense, “almost all” complex numbers are transcendental: there are uncountably many complex numbers, but only countably many algebraic numbers (

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