In mathematics,

equipollence is a concept in

set theory. Two sets are equipollent iff there is a

bijection from one to the other.

The symbol for this is a wavy equals-sign.

Informally, the two sets match each other in size. This is a precursor notion to being able to define the cardinality of a set. Being equipollent constitutes an equivalence relation on the class of sets:

The statement that A is equipollent to B may also be phrased as A and B

*have the same cardinality*, and a notion of

cardinality may be invoked, symbolized |A|, such that you can write that as |A| = |B|. But it requires substantially more work (including the

Cantor-Schröder-Bernstein Theorem) to be able to treat this "cardinality" as a

cardinal with all its properties.