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.