An Overview of the Cantor-Bernstein-Schroeder Theorem

A detailed tutorial on the Cantor-Bernstein-Schroeder Theorem. Step by step tutorial including several examples of the Cantor-Bernstein-Schroeder Theorem for reference.

The Cantor-Bernstein-Schroeder 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.  This means that if |A| < |B| and |B| < |A|, then they are equipollent. Equipollent is a term that is similar to equal, and is denoted in the same way. However, the word equipollent means equal in cardinality, but not in any other way.