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equipollence

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Definitions of equipollence in various dictionaries:

EQUIPOLLENCE - In mathematics, two sets or classes A and B are equinumerous if there exists a one-to-one correspondence (a bijection) between them, i.e. if there ex...

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Possible Dictionary Clues
The condition of being equipollent equality of power, force, signification, or application.
Sameness of signification of two or more propositions which differ in language.

Equipollence description
In mathematics, two sets or classes A and B are equinumerous if there exists a one-to-one correspondence (a bijection) between them, i.e. if there exists a function from A to B such that for every element y of B there is exactly one element x of A with f(x) = y. Equinumerous sets are said to have the same cardinality (number of elements). 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. * Equinumerosity has the characteristic properties of an equivalence relation. The statement that two sets A and B are equinumerous is usually denoted* * * * A * * B * * * * {\displaystyle A\approx B\,} * or * * * * A * * B * * * {\displaystyle A\sim B} * , or * * * * * \| * * A * * \| * * = * * \| *

Equipollence description

In mathematics, two sets or classes A and B are equinumerous if there exists a one-to-one correspondence (a bijection) between them, i.e. if there exists a function from A to B such that for every element y of B there is exactly one element x of A with f(x) = y. Equinumerous sets are said to have the same cardinality (number of elements). 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.
* Equinumerosity has the characteristic properties of an equivalence relation. The statement that two sets A and B are equinumerous is usually denoted*
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