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- Well-ordering_theorem abstract "In mathematics, the well-ordering theorem states that every set can be well-ordered. A set X is well-ordered by a strict total order if every non-empty subset of X has a least element under the ordering. This is also known as Zermelo's theorem and is equivalent to the Axiom of Choice. Ernst Zermelo introduced the Axiom of Choice as an "unobjectionable logical principle" to prove the well-ordering theorem. This is important because it makes every set susceptible to the powerful technique of transfinite induction. The well-ordering theorem has consequences that may seem paradoxical, such as the Banach–Tarski paradox.".
- Well-ordering_theorem wikiPageID "33458".
- Well-ordering_theorem wikiPageLength "5249".
- Well-ordering_theorem wikiPageOutDegree "23".
- Well-ordering_theorem wikiPageRevisionID "661191882".
- Well-ordering_theorem wikiPageWikiLink Axiom_of_Choice.
- Well-ordering_theorem wikiPageWikiLink Axiom_of_choice.
- Well-ordering_theorem wikiPageWikiLink Banach–Tarski_paradox.
- Well-ordering_theorem wikiPageWikiLink Category:Axiom_of_choice.
- Well-ordering_theorem wikiPageWikiLink Category:Theorems_in_the_foundations_of_mathematics.
- Well-ordering_theorem wikiPageWikiLink Ernst_Zermelo.
- Well-ordering_theorem wikiPageWikiLink Felix_Hausdorff.
- Well-ordering_theorem wikiPageWikiLink First-order_logic.
- Well-ordering_theorem wikiPageWikiLink First_order_logic.
- Well-ordering_theorem wikiPageWikiLink Georg_Cantor.
- Well-ordering_theorem wikiPageWikiLink Greatest_element.
- Well-ordering_theorem wikiPageWikiLink Gyula_Kőnig.
- Well-ordering_theorem wikiPageWikiLink Initial_segment.
- Well-ordering_theorem wikiPageWikiLink Least_element.
- Well-ordering_theorem wikiPageWikiLink Partially_ordered.
- Well-ordering_theorem wikiPageWikiLink Partially_ordered_set.
- Well-ordering_theorem wikiPageWikiLink Real_number.
- Well-ordering_theorem wikiPageWikiLink Second-order_logic.
- Well-ordering_theorem wikiPageWikiLink Second_order_logic.
- Well-ordering_theorem wikiPageWikiLink Set_(mathematics).
- Well-ordering_theorem wikiPageWikiLink Strict_total_order.
- Well-ordering_theorem wikiPageWikiLink Total_order.
- Well-ordering_theorem wikiPageWikiLink Transfinite_induction.
- Well-ordering_theorem wikiPageWikiLink Upper_set.
- Well-ordering_theorem wikiPageWikiLink Well-order.
- Well-ordering_theorem wikiPageWikiLink Well-ordering_principle.
- Well-ordering_theorem wikiPageWikiLink Zermelo–Fraenkel_axioms.
- Well-ordering_theorem wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- Well-ordering_theorem wikiPageWikiLink Zorns_Lemma.
- Well-ordering_theorem wikiPageWikiLink Zorns_lemma.
- Well-ordering_theorem wikiPageWikiLinkText "Well-ordering theorem".
- Well-ordering_theorem wikiPageWikiLinkText "Well–ordering theorem".
- Well-ordering_theorem wikiPageWikiLinkText "well-ordering principle".
- Well-ordering_theorem wikiPageWikiLinkText "well-ordering theorem".
- Well-ordering_theorem hasPhotoCollection Well-ordering_theorem.
- Well-ordering_theorem wikiPageUsesTemplate Template:Distinguish.
- Well-ordering_theorem wikiPageUsesTemplate Template:Redirect.
- Well-ordering_theorem subject Category:Axiom_of_choice.
- Well-ordering_theorem subject Category:Theorems_in_the_foundations_of_mathematics.
- Well-ordering_theorem type Theorem.
- Well-ordering_theorem type Thing.
- Well-ordering_theorem comment "In mathematics, the well-ordering theorem states that every set can be well-ordered. A set X is well-ordered by a strict total order if every non-empty subset of X has a least element under the ordering. This is also known as Zermelo's theorem and is equivalent to the Axiom of Choice. Ernst Zermelo introduced the Axiom of Choice as an "unobjectionable logical principle" to prove the well-ordering theorem.".
- Well-ordering_theorem label "Well-ordering theorem".
- Well-ordering_theorem differentFrom Well-ordering_principle.
- Well-ordering_theorem sameAs Zermelova_věta.
- Well-ordering_theorem sameAs Wohlordnungssatz.
- Well-ordering_theorem sameAs Teoremo_pri_bona_ordo.
- Well-ordering_theorem sameAs Zermelo_teoreem.
- Well-ordering_theorem sameAs قضیه_خوشترتیبی.
- Well-ordering_theorem sameAs Théorème_de_Zermelo.
- Well-ordering_theorem sameAs משפט_הסדר_הטוב.
- Well-ordering_theorem sameAs Jólrendezési_tétel.
- Well-ordering_theorem sameAs Teorema_del_buon_ordinamento.
- Well-ordering_theorem sameAs 정렬_정리.
- Well-ordering_theorem sameAs Welordeningsstelling.
- Well-ordering_theorem sameAs Twierdzenie_Zermelo.
- Well-ordering_theorem sameAs m.083jf.
- Well-ordering_theorem sameAs Teorema_de_bună_ordonare.
- Well-ordering_theorem sameAs Välordningssatsen.
- Well-ordering_theorem sameAs İyi_sıralılık_ilkesi.
- Well-ordering_theorem sameAs Q1457052.
- Well-ordering_theorem sameAs Q1457052.
- Well-ordering_theorem sameAs 良序定理.
- Well-ordering_theorem wasDerivedFrom Well-ordering_theorem?oldid=661191882.
- Well-ordering_theorem isPrimaryTopicOf Well-ordering_theorem.