**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

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Transitive set

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 |

Also known as

Ordinal

Child definitions