# inductive set

An inductive set^{} is a set $X$ with the property that, for every $x\in X$, the successor^{} ${x}^{\prime}$ of $x$ is also an element of $X$.

One major example of an inductive set is the set of natural numbers $\mathbb{N}$.

Title | inductive set |
---|---|

Canonical name | InductiveSet |

Date of creation | 2013-03-22 11:50:01 |

Last modified on | 2013-03-22 11:50:01 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 12 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 03E20 |

Classification | msc 45D05 |

Synonym | successor set |

Related topic | NaturalNumber |