Schröder-Bernstein theorem

Let S and T be sets. If there are injections ST and TS, then there is a bijection ST.

The Schröder-Bernstein theorem is useful for proving many results about cardinality, since it replaces one hard problem (finding a bijection between S and T) with two generally easier problems (finding two injections).

Title Schröder-Bernstein theorem
Canonical name SchroderBernsteinTheorem
Date of creation 2013-03-22 12:21:46
Last modified on 2013-03-22 12:21:46
Owner yark (2760)
Last modified by yark (2760)
Numerical id 9
Author yark (2760)
Entry type Theorem
Classification msc 03E10
Synonym Schroeder-Bernstein theorem
Synonym Cantor-Schroeder-Bernstein theorem
Synonym Cantor-Schröder-Bernstein theorem
Synonym Cantor-Bernstein theorem
Related topic AnInjectionBetweenTwoFiniteSetsOfTheSameCardinalityIsBijective
Related topic ProofOfSchroederBernsteinTheoremUsingTarskiKnasterTheorem