# pigeonhole principle

For any natural number^{} $n$, there does not exist a bijection between $n$ and a proper subset^{} of $n$.

The name of the theorem is based upon the observation that pigeons will not occupy a pigeonhole that already contains a pigeon, so there is no way to fit $n$ pigeons in fewer than $n$ pigeonholes.

Title | pigeonhole principle^{} |
---|---|

Canonical name | PigeonholePrinciple |

Date of creation | 2013-03-22 11:53:32 |

Last modified on | 2013-03-22 11:53:32 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 11 |

Author | djao (24) |

Entry type | Theorem |

Classification | msc 03E05 |

Classification | msc 03B22 |

Classification | msc 03-01 |

Classification | msc 03-00 |

Synonym | box principle |

Synonym | Dirichlet principle |