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- Regular_cardinal abstract "In set theory, a regular cardinal is a cardinal number that is equal to its own cofinality. So, crudely speaking, a regular cardinal is one which cannot be broken into a smaller collection of smaller parts.If the axiom of choice holds (so that any cardinal number can be well-ordered), an infinite cardinal is regular if and only if it cannot be expressed as the cardinal sum of a set of cardinality less than , the elements of which are cardinals less than . (The situation is slightly more complicated in contexts where the axiom of choice might fail; in that case not all cardinals are necessarily the cardinalities of well-ordered sets. In that case, the above definition is restricted to well-orderable cardinals only.) An infinite ordinal is regular if and only if it is a limit ordinal which is not the limit of a set of smaller ordinals which set has order type less than . A regular ordinal is always an initial ordinal, though some initial ordinals are not regular.Infinite well-ordered cardinals which are not regular are called singular cardinals. Finite cardinal numbers are typically not called regular or singular.".
- Regular_cardinal wikiPageID "374128".
- Regular_cardinal wikiPageRevisionID "580770025".
- Regular_cardinal hasPhotoCollection Regular_cardinal.
- Regular_cardinal subject Category:Cardinal_numbers.
- Regular_cardinal subject Category:Ordinal_numbers.
- Regular_cardinal type Abstraction100002137.
- Regular_cardinal type CardinalNumber113597585.
- Regular_cardinal type CardinalNumbers.
- Regular_cardinal type DefiniteQuantity113576101.
- Regular_cardinal type Measure100033615.
- Regular_cardinal type Number113582013.
- Regular_cardinal type OrdinalNumber113597280.
- Regular_cardinal type OrdinalNumbers.
- Regular_cardinal comment "In set theory, a regular cardinal is a cardinal number that is equal to its own cofinality. So, crudely speaking, a regular cardinal is one which cannot be broken into a smaller collection of smaller parts.If the axiom of choice holds (so that any cardinal number can be well-ordered), an infinite cardinal is regular if and only if it cannot be expressed as the cardinal sum of a set of cardinality less than , the elements of which are cardinals less than .".
- Regular_cardinal label "Cardinais regulares e singulares".
- Regular_cardinal label "Cardinal regular".
- Regular_cardinal label "Regular cardinal".
- Regular_cardinal label "Regularna liczba kardynalna".
- Regular_cardinal label "Regulier kardinaalgetal".
- Regular_cardinal label "正則基数".
- Regular_cardinal sameAs Regulární_ordinál.
- Regular_cardinal sameAs Cardinal_regular.
- Regular_cardinal sameAs 正則基数.
- Regular_cardinal sameAs 정칙기수.
- Regular_cardinal sameAs Regulier_kardinaalgetal.
- Regular_cardinal sameAs Regularna_liczba_kardynalna.
- Regular_cardinal sameAs Cardinais_regulares_e_singulares.
- Regular_cardinal sameAs m.020tkf.
- Regular_cardinal sameAs Q1193137.
- Regular_cardinal sameAs Q1193137.
- Regular_cardinal sameAs Regular_cardinal.
- Regular_cardinal wasDerivedFrom Regular_cardinal?oldid=580770025.
- Regular_cardinal isPrimaryTopicOf Regular_cardinal.