Meaning of Schröder-Bernstein theorem

Schrö'der-Bern'stein the"orem

Pronunciation: (shrō'dur-bûrn'stēn, -stīn, shrā'-), [key]
— Math. Math.
  1. the theorem of set theory that if two sets are so related that each can be placed in one-to-one correspondence with a subset of the other, then the sets are equivalent.
Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease.