# User Contributed Dictionary

## English

equipollent
1. having equal power or force
2. (of each of two statements) able to be deduced from the other
3. equivalent

# Extensive Definition

In the field of mathematics, two sets A and B are equinumerous if they have the same cardinality, i.e., if there exists a bijection f : A → B. This is usually denoted
A \approx B \, or A \sim B.
The study of cardinality is often called equinumerosity (equalness-of-number). The terms equipollence (equalness-of-strength) and equipotence (equalness-of-power) are sometimes used instead.
In Set, the category of all sets with functions as morphisms, an isomorphism between two sets is precisely a bijection, and two sets are equinumerous precisely if they are isomorphic in this category.