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- Q1033910 subject Q18550470.
- Q1033910 subject Q8266681.
- Q1033910 subject Q8343923.
- Q1033910 abstract "In set theory, the Schröder–Bernstein theorem, named after 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 Cantor–Bernstein theorem, or the Cantor–Schroeder–Bernstein theorem (named after Georg Cantor).This theorem 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 are therefore rejected by intuitionists.".
- Q1033910 thumbnail Cantor-Bernstein.png?width=300.
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- Q1033910 wikiPageWikiLink Q8266681.
- Q1033910 wikiPageWikiLink Q8343923.
- Q1033910 wikiPageWikiLink Q860611.
- Q1033910 comment "In set theory, the Schröder–Bernstein theorem, named after 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.".
- Q1033910 label "Schröder–Bernstein theorem".
- Q1033910 depiction Cantor-Bernstein.png.
