# transitive closure

The *transitive closure ^{}* of a set $X$ is the smallest transitive set $\mathrm{tc}(X)$ such that $X\subseteq \mathrm{tc}(X)$.

The transitive closure of a set can be constructed as follows:

Define a function $f$ on $\omega $ by $f(0)=X$ and $f(n+1)=\bigcup f(n)$

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Title | transitive closure |
---|---|

Canonical name | TransitiveClosure |

Date of creation | 2013-03-22 13:04:33 |

Last modified on | 2013-03-22 13:04:33 |

Owner | Henry (455) |

Last modified by | Henry (455) |

Numerical id | 4 |

Author | Henry (455) |

Entry type | Definition |

Classification | msc 03E20 |

Related topic | Transitive^{} |