<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)
Nearby terms:
von Neumann integer « von Neumann, John « von Neumann machine « von Neumann ordinal » voodoo programming » Voronoi diagram » Voronoi polygon
