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von neumann ordinal

von neumann ordinal in Technology
mathematics
An implementation of ordinals in set theory (e.g. Zermelo Fränkel set theory or ZFC). The von Neumann ordinal alpha is the well-ordered set containing just the ordinals "shorter" than alpha.
"Reasonable" set theories (like ZF) include Mostowski's Collapsing Theorem: any well-ordered set is isomorphic to a von Neumann ordinal. In really screwy theories (e.g. NFU -- New Foundations with Urelemente) this theorem is false.
The finite von Neumann ordinals are the von Neumann integers.
(1995-03-30)
The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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