AskDefine | Define equipollent

User Contributed Dictionary

English

Adjective

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.

See also

equipollent in Bulgarian: Равномощно множество
equipollent in Catalan: Equipotència
equipollent in French: Équipotence
equipollent in Croatian: Jednakobrojnost
equipollent in Occitan (post 1500): Equipoténcia
equipollent in Serbian: Еквипотенција
equipollent in Chinese: 等势
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