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Schröder-Bernstein Theorem

The Schröder-Bernstein theorem for numbers states that if

n\leq m\leq 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).

See also Bijection, Equipollent, Injection

© 1996-9 Eric W. Weisstein