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- Cantors_paradox abstract "In set theory, Cantor's paradox is derivable from the theorem that there is no greatest cardinal number, so that the collection of "infinite sizes" is itself infinite. The difficulty is handled in axiomatic set theory by declaring that this collection is not a set but a proper class; in von Neumann–Bernays–Gödel set theory it follows from this and the axiom of limitation of size that this proper class must be in bijection with the class of all sets. Thus, not only are there infinitely many infinities, but this infinity is larger than any of the infinities it enumerates.This paradox is named for Georg Cantor, who is often credited with first identifying it in 1899 (or between 1895 and 1897). Like a number of "paradoxes" it is not actually contradictory but merely indicative of a mistaken intuition, in this case about the nature of infinity and the notion of a set. Put another way, it is paradoxical within the confines of naïve set theory and therefore demonstrates that a careless axiomatization of this theory is inconsistent.".
- Cantors_paradox wikiPageExternalLink 496807.html.
- Cantors_paradox wikiPageExternalLink CantorsParadox.html.
- Cantors_paradox wikiPageID "2732904".
- Cantors_paradox wikiPageLength "4915".
- Cantors_paradox wikiPageOutDegree "25".
- Cantors_paradox wikiPageRevisionID "682123172".
- Cantors_paradox wikiPageWikiLink Axiom_of_limitation_of_size.
- Cantors_paradox wikiPageWikiLink Bertrand_Russell.
- Cantors_paradox wikiPageWikiLink Bijection.
- Cantors_paradox wikiPageWikiLink Burali-Forti_paradox.
- Cantors_paradox wikiPageWikiLink Cantors_theorem.
- Cantors_paradox wikiPageWikiLink Cardinal_number.
- Cantors_paradox wikiPageWikiLink Category:Georg_Cantor.
- Cantors_paradox wikiPageWikiLink Category:Paradoxes_of_naive_set_theory.
- Cantors_paradox wikiPageWikiLink Class_(set_theory).
- Cantors_paradox wikiPageWikiLink Georg_Cantor.
- Cantors_paradox wikiPageWikiLink List_of_order_structures_in_mathematics.
- Cantors_paradox wikiPageWikiLink Naive_set_theory.
- Cantors_paradox wikiPageWikiLink Naïve_set_theory.
- Cantors_paradox wikiPageWikiLink Ordered_set.
- Cantors_paradox wikiPageWikiLink Ordinal_number.
- Cantors_paradox wikiPageWikiLink Ordinal_numbers.
- Cantors_paradox wikiPageWikiLink Paradox.
- Cantors_paradox wikiPageWikiLink Power_set.
- Cantors_paradox wikiPageWikiLink Proper_class.
- Cantors_paradox wikiPageWikiLink Set_theory.
- Cantors_paradox wikiPageWikiLink Theorem.
- Cantors_paradox wikiPageWikiLink Von_Neumann–Bernays–Gödel_set_theory.
- Cantors_paradox wikiPageWikiLink ZFC.
- Cantors_paradox wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- Cantors_paradox wikiPageWikiLinkText "Cantor".
- Cantors_paradox wikiPageWikiLinkText "Cantor's paradox".
- Cantors_paradox wikiPageWikiLinkText "Cantor's".
- Cantors_paradox wikiPageWikiLinkText "The paradox of the greatest cardinal".
- Cantors_paradox wikiPageWikiLinkText "paradox".
- Cantors_paradox hasPhotoCollection Cantors_paradox.
- Cantors_paradox wikiPageUsesTemplate Template:Cite_book.
- Cantors_paradox wikiPageUsesTemplate Template:Cite_journal.
- Cantors_paradox subject Category:Georg_Cantor.
- Cantors_paradox subject Category:Paradoxes_of_naive_set_theory.
- Cantors_paradox comment "In set theory, Cantor's paradox is derivable from the theorem that there is no greatest cardinal number, so that the collection of "infinite sizes" is itself infinite. The difficulty is handled in axiomatic set theory by declaring that this collection is not a set but a proper class; in von Neumann–Bernays–Gödel set theory it follows from this and the axiom of limitation of size that this proper class must be in bijection with the class of all sets.".
- Cantors_paradox label "Cantor's paradox".
- Cantors_paradox sameAs Cantorův_paradox.
- Cantors_paradox sameAs Cantorsche_Antinomie.
- Cantors_paradox sameAs Paradokso_de_Russell.
- Cantors_paradox sameAs Paradoxe_de_Cantor.
- Cantors_paradox sameAs הפרדוקס_של_קנטור.
- Cantors_paradox sameAs Cantor-paradoxon.
- Cantors_paradox sameAs Paradosso_di_Cantor.
- Cantors_paradox sameAs 칸토어_역설.
- Cantors_paradox sameAs Paradox_van_Cantor.
- Cantors_paradox sameAs Paradoks_zbioru_wszystkich_zbiorów.
- Cantors_paradox sameAs Paradoxo_de_Cantor.
- Cantors_paradox sameAs m.07_q75.
- Cantors_paradox sameAs Парадокс_Кантора.
- Cantors_paradox sameAs Cantorov_paradox.
- Cantors_paradox sameAs Cantor_paradoksu.
- Cantors_paradox sameAs Парадокс_Кантора.
- Cantors_paradox sameAs Q379078.
- Cantors_paradox sameAs Q379078.
- Cantors_paradox sameAs 康托尔悖论.
- Cantors_paradox wasDerivedFrom Cantors_paradoxoldid=682123172.
- Cantors_paradox isPrimaryTopicOf Cantors_paradox.