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- Von_Neumann_cardinal_assignment abstract "The von Neumann cardinal assignment is a cardinal assignment which uses ordinal numbers. For a well-ordered set U, we define its cardinal number to be the smallest ordinal number equinumerous to U. More precisely:where ON is the class of ordinals. This ordinal is also called the initial ordinal of the cardinal.That such an ordinal exists and is unique is guaranteed by the fact that U is well-orderable and that the class of ordinals is well-ordered, using the axiom of replacement. With the full axiom of choice, every set is well-orderable, so every set has a cardinal; we order the cardinals using the inherited ordering from the ordinal numbers. This is readily found to coincide with the ordering via ≤c. This is a well-ordering of cardinal numbers.".
- Von_Neumann_cardinal_assignment wikiPageID "373174".
- Von_Neumann_cardinal_assignment wikiPageRevisionID "546176102".
- Von_Neumann_cardinal_assignment hasPhotoCollection Von_Neumann_cardinal_assignment.
- Von_Neumann_cardinal_assignment subject Category:Cardinal_numbers.
- Von_Neumann_cardinal_assignment subject Category:Ordinal_numbers.
- Von_Neumann_cardinal_assignment type Abstraction100002137.
- Von_Neumann_cardinal_assignment type CardinalNumber113597585.
- Von_Neumann_cardinal_assignment type CardinalNumbers.
- Von_Neumann_cardinal_assignment type DefiniteQuantity113576101.
- Von_Neumann_cardinal_assignment type Measure100033615.
- Von_Neumann_cardinal_assignment type Number113582013.
- Von_Neumann_cardinal_assignment type OrdinalNumber113597280.
- Von_Neumann_cardinal_assignment type OrdinalNumbers.
- Von_Neumann_cardinal_assignment comment "The von Neumann cardinal assignment is a cardinal assignment which uses ordinal numbers. For a well-ordered set U, we define its cardinal number to be the smallest ordinal number equinumerous to U. More precisely:where ON is the class of ordinals. This ordinal is also called the initial ordinal of the cardinal.That such an ordinal exists and is unique is guaranteed by the fact that U is well-orderable and that the class of ordinals is well-ordered, using the axiom of replacement.".
- Von_Neumann_cardinal_assignment label "Von Neumann cardinal assignment".
- Von_Neumann_cardinal_assignment label "冯·诺伊曼基数指派".
- Von_Neumann_cardinal_assignment sameAs m.020q3y.
- Von_Neumann_cardinal_assignment sameAs Q7941494.
- Von_Neumann_cardinal_assignment sameAs Q7941494.
- Von_Neumann_cardinal_assignment sameAs Von_Neumann_cardinal_assignment.
- Von_Neumann_cardinal_assignment wasDerivedFrom Von_Neumann_cardinal_assignment?oldid=546176102.
- Von_Neumann_cardinal_assignment isPrimaryTopicOf Von_Neumann_cardinal_assignment.