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- Cantor–Bernstein–Schroeder_theorem abstract "In set theory, the Cantor–Bernstein–Schroeder theorem, named after Georg Cantor, Felix Bernstein, and Ernst Schröder, states that, if there exist injective functions f : A → B and g : B → A between the sets A and B, then there exists a bijective function h : A → B. In terms of the cardinality of the two sets, this means that if |A| ≤ |B| and |B| ≤ |A|, then |A| = |B|; that is, A and B are equipollent. This is a useful feature in the ordering of cardinal numbers.The theorem is also known as the Schroeder–Bernstein theorem, the Cantor–Bernstein theorem, or the Cantor–Schroeder–Bernstein theorem. An important feature of this theorem is that it does not rely on the axiom of choice. However, its various proofs are non-constructive, as they depend on the law of excluded middle, and therefore rejected by intuitionists.".
- Cantor–Bernstein–Schroeder_theorem thumbnail Cantor-Bernstein.png?width=300.
- Cantor–Bernstein–Schroeder_theorem wikiPageID "164503".
- Cantor–Bernstein–Schroeder_theorem wikiPageRevisionID "606598372".
- Cantor–Bernstein–Schroeder_theorem id "3156".
- Cantor–Bernstein–Schroeder_theorem id "Cantor-Schroeder-Bernstein+theorem".
- Cantor–Bernstein–Schroeder_theorem title "Cantor-Schroeder-Bernstein theorem".
- Cantor–Bernstein–Schroeder_theorem title "Proof of the Bernstein–Schroeder theorem".
- Cantor–Bernstein–Schroeder_theorem title "Schröder-Bernstein Theorem".
- Cantor–Bernstein–Schroeder_theorem title "Schröder-Bernstein theorem".
- Cantor–Bernstein–Schroeder_theorem urlname "Schroeder-BernsteinTheorem".
- Cantor–Bernstein–Schroeder_theorem urlname "schroderbernsteintheorem".
- Cantor–Bernstein–Schroeder_theorem subject Category:Articles_containing_proofs.
- Cantor–Bernstein–Schroeder_theorem subject Category:Cardinal_numbers.
- Cantor–Bernstein–Schroeder_theorem subject Category:Theorems_in_the_foundations_of_mathematics.
- Cantor–Bernstein–Schroeder_theorem comment "In set theory, the Cantor–Bernstein–Schroeder theorem, named after Georg Cantor, Felix Bernstein, and Ernst Schröder, states that, if there exist injective functions f : A → B and g : B → A between the sets A and B, then there exists a bijective function h : A → B. In terms of the cardinality of the two sets, this means that if |A| ≤ |B| and |B| ≤ |A|, then |A| = |B|; that is, A and B are equipollent.".
- Cantor–Bernstein–Schroeder_theorem label "Cantor–Bernstein–Schroeder theorem".
- Cantor–Bernstein–Schroeder_theorem label "Satz von Cantor-Bernstein-Schröder".
- Cantor–Bernstein–Schroeder_theorem label "Stelling van Cantor-Bernstein-Schröder".
- Cantor–Bernstein–Schroeder_theorem label "Teorema de Cantor-Bernstein-Schroeder".
- Cantor–Bernstein–Schroeder_theorem label "Teorema de Cantor-Bernstein-Schröder".
- Cantor–Bernstein–Schroeder_theorem label "Teorema di Cantor-Bernstein-Schröder".
- Cantor–Bernstein–Schroeder_theorem label "Théorème de Cantor-Bernstein".
- Cantor–Bernstein–Schroeder_theorem label "Twierdzenie Cantora-Bernsteina-Schrödera".
- Cantor–Bernstein–Schroeder_theorem label "Теорема Кантора — Бернштейна".
- Cantor–Bernstein–Schroeder_theorem label "ベルンシュタインの定理".
- Cantor–Bernstein–Schroeder_theorem label "康托尔－伯恩斯坦－施罗德定理".
- Cantor–Bernstein–Schroeder_theorem sameAs Cantor%E2%80%93Bernstein%E2%80%93Schroeder_theorem.
- Cantor–Bernstein–Schroeder_theorem sameAs Cantorova-Bernsteinova_věta.
- Cantor–Bernstein–Schroeder_theorem sameAs Satz_von_Cantor-Bernstein-Schröder.
- Cantor–Bernstein–Schroeder_theorem sameAs Teorema_de_Cantor-Bernstein-Schröder.
- Cantor–Bernstein–Schroeder_theorem sameAs Théorème_de_Cantor-Bernstein.
- Cantor–Bernstein–Schroeder_theorem sameAs Teorema_di_Cantor-Bernstein-Schröder.
- Cantor–Bernstein–Schroeder_theorem sameAs ベルンシュタインの定理.
- Cantor–Bernstein–Schroeder_theorem sameAs Stelling_van_Cantor-Bernstein-Schröder.
- Cantor–Bernstein–Schroeder_theorem sameAs Twierdzenie_Cantora-Bernsteina-Schrödera.
- Cantor–Bernstein–Schroeder_theorem sameAs Teorema_de_Cantor-Bernstein-Schroeder.
- Cantor–Bernstein–Schroeder_theorem sameAs Q1033910.
- Cantor–Bernstein–Schroeder_theorem sameAs Q1033910.
- Cantor–Bernstein–Schroeder_theorem wasDerivedFrom Cantor–Bernstein–Schroeder_theorem?oldid=606598372.
- Cantor–Bernstein–Schroeder_theorem depiction Cantor-Bernstein.png.
