ThmDex – An index of mathematical definitions, results, and conjectures.
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