**ordinal number**if and only if

(1) | $X$ is a D666: Transitive set |

(2) | ${\in}_X$ is the D1943: Membership relation on $X$ |

(3) | $P$ is a D1124: Well-ordered set |

▼ | Set of symbols |

▼ | Alphabet |

▼ | Deduction system |

▼ | Theory |

▼ | Zermelo-Fraenkel set theory |

▼ | Set |

▼ | Transitive set |

Definition D672

Ordinal number

Formulation 0

An D548: Ordered pair $P = (X, {\in}_X)$ is an **ordinal number** if and only if

(1) | $X$ is a D666: Transitive set |

(2) | ${\in}_X$ is the D1943: Membership relation on $X$ |

(3) | $P$ is a D1124: Well-ordered set |

Children

▶ | Class of ordinal numbers |