# partition

A *partition ^{}* $P$ of a set $S$ is a collection

^{}of pairwise disjoint nonempty sets such that $\cup P=S$.

Any partition $P$ of a set $S$ introduces an equivalence relation^{} on $S$, where each $A\in P$ is an equivalence class^{}. Similarly, given an equivalence relation on $S$, the collection of distinct equivalence classes is a partition of $S$.

Title | partition |

Canonical name | Partition |

Date of creation | 2013-03-22 11:49:05 |

Last modified on | 2013-03-22 11:49:05 |

Owner | Wkbj79 (1863) |

Last modified by | Wkbj79 (1863) |

Numerical id | 11 |

Author | Wkbj79 (1863) |

Entry type | Definition |

Classification | msc 03-00 |

Classification | msc 45D05 |

Synonym | set partition |

Related topic | EquivalenceRelation |

Related topic | EquivalenceClass |

Related topic | BeattysTheorem |

Related topic | Coloring^{} |