ordinal number

An ordinal numberMathworldPlanetmath is a well ordered set S such that, for every xS,


(where < is the ordering relation on S).

It follows immediately from the definition that every ordinal is a transitive set. Also note that if a,bS then we have a<b if and only if ab.

There is a theory of ordinal arithmetic which allows construction of various ordinals. For example, all the numbers 0, 1, 2, …have natural interpretationsMathworldPlanetmathPlanetmath as ordinals, as does the set of natural numbers (including 0), which in this context is often denoted by ω, and is the first infiniteMathworldPlanetmath 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