ThmDex – An index of mathematical definitions, results, and conjectures.
▼ 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
Definition D1707
Ordered set
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
Children
▶ D714: Dedekind cut