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In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, n th, etc.) aimed to extend enumeration to infinite sets. [1]
Ordinal indicator – Character(s) following an ordinal number (used when writing ordinal numbers, such as a super-script) Ordinal number – Generalization of "n-th" to infinite cases (the related, but more formal and abstract, usage in mathematics) Ordinal data, in statistics; Ordinal date – Date written as number of days since first day of ...
Every well-ordered set is order-equivalent to exactly one ordinal number, by definition. The ordinal numbers are taken to be the canonical representatives of their classes, and so the order type of a well-ordered set is usually identified with the corresponding ordinal. Order types thus often take the form of arithmetic expressions of ordinals.
The von Neumann cardinal assignment is a cardinal assignment that uses ordinal numbers.For a well-orderable set U, we define its cardinal number to be the smallest ordinal number equinumerous to U, using the von Neumann definition of an ordinal number.
In other words, every ordinal number α can be uniquely written as + + +, where k is a natural number, and … are ordinal numbers. Another variation of the Cantor normal form is the "base δ expansion", where ω is replaced by any ordinal δ > 1 , and the numbers c i are nonzero ordinals less than δ .
Pages in category "Ordinal numbers" The following 51 pages are in this category, out of 51 total. This list may not reflect recent changes. ...
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