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- Hartogs_number abstract "In mathematics, specifically in axiomatic set theory, a Hartogs number is a particular kind of cardinal number. It was shown by Friedrich Hartogs in 1915, from ZF alone (that is, without using the axiom of choice), that there is a least well-ordered cardinal greater than a given well-ordered cardinal.To define the Hartogs number of a set it is not in fact necessary that the set be well-orderable: If X is any set, then the Hartogs number of X is the least ordinal α such that there is no injection from α into X. If X cannot be well-ordered, then we can no longer say that this α is the least well-ordered cardinal greater than the cardinality of X, but it remains the least well-ordered cardinal not less than or equal to the cardinality of X. The map taking X to α is sometimes called Hartogs' function.".
- Hartogs_number wikiPageExternalLink ast_notes_4.pdf.
- Hartogs_number wikiPageExternalLink www.digizeitschriften.de.
- Hartogs_number wikiPageExternalLink ?PPN=GDZPPN002266105.
- Hartogs_number wikiPageID "2977752".
- Hartogs_number wikiPageLength "3274".
- Hartogs_number wikiPageOutDegree "23".
- Hartogs_number wikiPageRevisionID "671323333".
- Hartogs_number wikiPageWikiLink Axiom_of_choice.
- Hartogs_number wikiPageWikiLink Axiom_of_power_set.
- Hartogs_number wikiPageWikiLink Axiom_schema_of_replacement.
- Hartogs_number wikiPageWikiLink Axiom_schema_of_separation.
- Hartogs_number wikiPageWikiLink Axiom_schema_of_specification.
- Hartogs_number wikiPageWikiLink Axiomatic_set_theory.
- Hartogs_number wikiPageWikiLink Cardinal_number.
- Hartogs_number wikiPageWikiLink Category:Cardinal_numbers.
- Hartogs_number wikiPageWikiLink Category:Set_theory.
- Hartogs_number wikiPageWikiLink Domain_(mathematics).
- Hartogs_number wikiPageWikiLink Domain_of_a_function.
- Hartogs_number wikiPageWikiLink Friedrich_Hartogs.
- Hartogs_number wikiPageWikiLink Injective_function.
- Hartogs_number wikiPageWikiLink Map_(mathematics).
- Hartogs_number wikiPageWikiLink Mathematics.
- Hartogs_number wikiPageWikiLink Mathematische_Annalen.
- Hartogs_number wikiPageWikiLink Order_type.
- Hartogs_number wikiPageWikiLink Ordinal_number.
- Hartogs_number wikiPageWikiLink Power_set.
- Hartogs_number wikiPageWikiLink Reflexive_relation.
- Hartogs_number wikiPageWikiLink Set_theory.
- Hartogs_number wikiPageWikiLink Transitive_set.
- Hartogs_number wikiPageWikiLink Well-order.
- Hartogs_number wikiPageWikiLink Well-ordered.
- Hartogs_number wikiPageWikiLink Zermelo-Fraenkel_set_theory.
- Hartogs_number wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- Hartogs_number wikiPageWikiLinkText "Hartogs number".
- Hartogs_number wikiPageWikiLinkText "Hartogs' lemma".
- Hartogs_number wikiPageWikiLinkText "Hartogs' theorem".
- Hartogs_number hasPhotoCollection Hartogs_number.
- Hartogs_number wikiPageUsesTemplate Template:Cite_book.
- Hartogs_number wikiPageUsesTemplate Template:Cite_journal.
- Hartogs_number wikiPageUsesTemplate Template:Cite_web.
- Hartogs_number wikiPageUsesTemplate Template:Settheory-stub.
- Hartogs_number subject Category:Cardinal_numbers.
- Hartogs_number subject Category:Set_theory.
- Hartogs_number hypernym Kind.
- Hartogs_number comment "In mathematics, specifically in axiomatic set theory, a Hartogs number is a particular kind of cardinal number.".
- Hartogs_number label "Hartogs number".
- Hartogs_number sameAs Satz_von_Hartogs_(Mengenlehre).
- Hartogs_number sameAs Número_de_Hartogs.
- Hartogs_number sameAs Ordinal_de_Hartogs.
- Hartogs_number sameAs מספר_הרטוגס.
- Hartogs_number sameAs ハルトークス数.
- Hartogs_number sameAs 하르톡스_수.
- Hartogs_number sameAs Twierdzenie_Hartogsa_(teoria_mnogości).
- Hartogs_number sameAs Número_de_Hartogs.
- Hartogs_number sameAs m.08h94y.
- Hartogs_number sameAs Q1186007.
- Hartogs_number sameAs Q1186007.
- Hartogs_number wasDerivedFrom Hartogs_number?oldid=671323333.
- Hartogs_number isPrimaryTopicOf Hartogs_number.