Ordinal: Difference between revisions

In set theory, the '''ordinal numbers''' or '''ordinals''' are an extension of the [[natural numbers]] that describe the order types of [[Well-ordered set|well-ordered sets]]. A set \( S \) is '''well-ordered''' if each non-empty \( T \subseteq S \) has a least element. For example, any finite set of real numbers is well-ordered, as well as the set of natural numbers, while neither the set of nonnegative rationals nor the set of integers is well-ordered.