**ordered set**if and only if

(1) | $X$ is a D11: Set |

(2) | ${\preceq}$ is an D378: Ordering relation on $X$ |

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Binary endorelation

▾ Preordering relation

▾ Partial ordering relation

▾ Ordering relation

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Binary endorelation

▾ Preordering relation

▾ Partial ordering relation

▾ Ordering relation

Formulation 0

An D548: Ordered pair $P = (X, {\preceq})$ is an **ordered set** if and only if

(1) | $X$ is a D11: Set |

(2) | ${\preceq}$ is an D378: Ordering relation on $X$ |

Also known as

Totally ordered set, Toset, Linearly ordered set

Child definitions