Schröder–Bernstein theorem
In set theory, the Schröder–Bernstein theorem 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 classically implies that if |A| ≤ |B| and |B| ≤ |A|, then |A| = |B|; that is, A and B are equipotent. This is a useful feature in the ordering of cardinal numbers.
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(Cantor-)Schröder-Bernstein theorem(Cantor–)Schröder–Bernstein theoremBernstein-Schroeder theoremBernstein–Schroeder theoremCantor-Bernstein-Schroder theoremCantor-Bernstein-Schroeder theoremCantor-Bernstein-Schröder theoremCantor-Berstein theoremCantor-Schroder-Bernstein theoremCantor-Schroeder-Bernstein theoremCantor-Schroeder-Berntein theoremCantor-Schroeder-Berstein theoremCantor-Schröder-Bernstein theoremCantor Schroeder Bernstein TheoremCantor–Bernstein–Schroder theoremCantor–Bernstein–Schroeder theoremCantor–Bernstein–Schröder theoremCantor–Schroeder–Bernstein theoremCantor–Schröder–Bernstein theoremSchroder-Bernstein TheoremSchroder-Bernstein theoremSchroder–Bernstein TheoremSchroder–Bernstein theoremSchroeder-Bernstein theoremSchroeder–Bernstein theoremSchröder-Bernstein TheoremSchröder-Bernstein theoremSchröder–Bernstein TheoremShroeder-Bernstein theoremShroeder–Bernstein theorem
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(Cantor-)Schröder-Bernstein theorem(Cantor–)Schröder–Bernstein theoremAxiom of choiceBanach–Tarski paradoxBernstein's theoremBernstein-Schroeder theoremBernstein–Schroeder theoremBijectionBijective proofCantor's diagonal argumentCantor's theoremCantor's theorem (disambiguation)Cantor-Bernstein-Schroder theoremCantor-Bernstein-Schroeder theoremCantor-Bernstein-Schröder theoremCantor-Berstein theoremCantor-Schroder-Bernstein theoremCantor-Schroeder-Bernstein theoremCantor-Schroeder-Berntein theoremCantor-Schroeder-Berstein theoremCantor-Schröder-Bernstein theoremCantor Schroeder Bernstein TheoremCantor setCantor–Bernstein–Schroder theoremCantor–Bernstein–Schroeder theoremCantor–Bernstein–Schröder theoremCantor–Schroeder–Bernstein theoremCantor–Schröder–Bernstein theoremCardinal assignmentCardinal numberCardinalityCardinality of the continuumConstructivism (philosophy of mathematics)Eilenberg–Mazur swindleEquinumerosityErnst SchröderFelix Bernstein (mathematician)Georg CantorGroup structure and the axiom of choiceImplementation of mathematics in set theory
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Schröder–Bernstein theorem
In set theory, the Schröder–Bernstein theorem 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 classically implies that if |A| ≤ |B| and |B| ≤ |A|, then |A| = |B|; that is, A and B are equipotent. This is a useful feature in the ordering of cardinal numbers.
has abstract
Cantorova-Bernsteinova věta (t ...... návání nekonečných mohutností.
@cs
El Teorema de Schröder-Bernste ...... el seu llibre sobre funcions.
@ca
El teorema de Schröder y Berns ...... ndencia biunívoca entre ellos.
@es
Em teoria de conjuntos, o Teor ...... depende do axioma da escolha.
@pt
In de axiomatische verzameling ...... x Bernstein en Ernst Schröder'
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In matematica, il teorema di C ...... siste una funzione biiettiva .
@it
In set theory, the Schröder–Be ...... st published it without proof.
@en
Le théorème de Cantor-Bernstei ...... ptées par les intuitionnistes.
@fr
Twierdzenie Cantora-Bernsteina ...... ch kardynalnych: Jeśli oraz to
@pl
Теоре́ма Ка́нтора — Бернште́йн ...... что где — кардинальные числа.
@ru
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id
Cantor-Schroeder-Bernstein+theorem
@en
title
Cantor-Schroeder-Bernstein theorem
@en
Schröder-Bernstein Theorem
@en
urlname
Schroeder-BernsteinTheorem
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wikiPageUsesTemplate
hypernym
comment
Cantorova-Bernsteinova věta (t ...... návání nekonečných mohutností.
@cs
El Teorema de Schröder-Bernste ...... eshores A i B són equivalents.
@ca
El teorema de Schröder y Berns ...... voca entre B y A. Formalmente:
@es
Em teoria de conjuntos, o Teor ...... depende do axioma da escolha.
@pt
In de axiomatische verzameling ...... x Bernstein en Ernst Schröder'
@nl
In matematica, il teorema di C ...... siste una funzione biiettiva .
@it
In set theory, the Schröder–Be ...... ordering of cardinal numbers.
@en
Le théorème de Cantor-Bernstei ...... iste une bijection de E sur F.
@fr
Twierdzenie Cantora-Bernsteina ...... ch kardynalnych: Jeśli oraz to
@pl
Теоре́ма Ка́нтора — Бернште́йн ...... что где — кардинальные числа.
@ru
label
Cantorova–Bernsteinova věta
@cs
Satz von Cantor-Bernstein-Schröder
@de
Schröder–Bernstein theorem
@en
Stelling van Cantor-Bernstein-Schröder
@nl
Teorema de Cantor-Bernstein-Schroeder
@pt
Teorema de Cantor-Bernstein-Schröder
@es
Teorema de Schröder-Bernstein
@ca
Teorema di Cantor-Bernstein-Schröder
@it
Théorème de Cantor-Bernstein
@fr
Twierdzenie Cantora-Bernsteina-Schrödera
@pl