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.
Schröder–Bernstein theorem - Wikipedia Jump to content From Wikipedia, the free encyclopedia Theorem in set theory 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
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