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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 wikiPageRevisionID "599391646".
- Well-ordering_theorem hasPhotoCollection Well-ordering_theorem.
- Well-ordering_theorem subject Category:Axiom_of_choice.
- Well-ordering_theorem subject Category:Theorems_in_the_foundations_of_mathematics.
- Well-ordering_theorem type Abstraction100002137.
- Well-ordering_theorem type Communication100033020.
- Well-ordering_theorem type Message106598915.
- Well-ordering_theorem type Proposition106750804.
- Well-ordering_theorem type Statement106722453.
- Well-ordering_theorem type Theorem106752293.
- Well-ordering_theorem type TheoremsInTheFoundationsOfMathematics.
- 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 "Teorema del buon ordinamento".
- Well-ordering_theorem label "Théorème de Zermelo".
- Well-ordering_theorem label "Twierdzenie Zermelo".
- Well-ordering_theorem label "Well-ordering theorem".
- Well-ordering_theorem label "Welordeningsstelling".
- Well-ordering_theorem label "Wohlordnungssatz".
- Well-ordering_theorem label "良序定理".
- Well-ordering_theorem sameAs Zermelova_věta.
- Well-ordering_theorem sameAs Wohlordnungssatz.
- Well-ordering_theorem sameAs Théorème_de_Zermelo.
- Well-ordering_theorem sameAs Teorema_del_buon_ordinamento.
- Well-ordering_theorem sameAs Welordeningsstelling.
- Well-ordering_theorem sameAs Twierdzenie_Zermelo.
- Well-ordering_theorem sameAs m.083jf.
- Well-ordering_theorem sameAs Q1457052.
- Well-ordering_theorem sameAs Q1457052.
- Well-ordering_theorem sameAs Well-ordering_theorem.
- Well-ordering_theorem wasDerivedFrom Well-ordering_theorem?oldid=599391646.
- Well-ordering_theorem isPrimaryTopicOf Well-ordering_theorem.