The Schröder-Bernstein theorem for numbers states that if n<=m<=n, then m = n. For sets, the theorem states that if there are injections of the set A into the set B and of B into A, then there is a bijective correspondence between A and B (i.e., they are equipollent).

bijection | cardinal comparison | equipollent | injection | trichotomy law

Sergei Natanovich Bernstein