# 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 |