ordinal number
An ordinal number is a well ordered set such that, for every ,
(where is the ordering relation on ).
It follows immediately from the definition that every ordinal is a transitive set. Also note that if then we have if and only if .
There is a theory of ordinal arithmetic which allows construction of various ordinals. For example, all the numbers , , , …have natural interpretations as ordinals, as does the set of natural numbers (including ), which in this context is often denoted by , and is the first infinite ordinal.
Title | ordinal number |
---|---|
Canonical name | OrdinalNumber |
Date of creation | 2013-03-22 12:07:55 |
Last modified on | 2013-03-22 12:07:55 |
Owner | yark (2760) |
Last modified by | yark (2760) |
Numerical id | 8 |
Author | yark (2760) |
Entry type | Definition |
Classification | msc 03E10 |
Synonym | ordinal |
Related topic | VonNeumannOrdinal |