Definition:Ordinal

Also known as
An ordinal is also known as an ordinal number.

For a given well-ordered set $\struct {X, \preceq}$, the expression:
 * $\map {\operatorname {Ord} } X$

can be used to denote the unique ordinal which is order isomorphic to $\struct {X, \preceq}$.

Also see

 * Equivalence of Definitions of Ordinal


 * Woset is Isomorphic to Unique Ordinal


 * Ordering on Ordinal is Subset Relation where it is shown that $\forall a, b \in S$, the following statements are equivalent:
 * $b \prec a$
 * $b \subsetneqq a$
 * $b \in a$


 * Ordinal is Set of all Smaller Ordinals

It is customary to denote the ordering relation between ordinals as $\le$ rather than $\subseteq$ or $\preceq$.