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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.

E`qui*pol"lent (?), a. [L. aequipollens; aequus equal + pollens, -entis, p. pr. of pollere to be strong, able: cf. F. 'equipollent.]

1.

Having equal power or force; equivalent.

Bacon.

2. Logic

Having equivalent signification and reach; expressing the same thing, but differently.

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