Karl Jones: Created page with "In mathematics, two sets A and B are '''equinumerous''' if there exists a one-to-one correspondence (a bijection) between them, i.e. if there exi..."

2016-09-22T16:20:46Z

Created page with "In mathematics, two sets A and B are '''equinumerous''' if there exists a one-to-one correspondence (a bijection) between them, i.e. if there exi..."

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In [[mathematics]], two [[Set (mathematics)|sets]] A and B are '''equinumerous''' if there exists a one-to-one correspondence (a [[bijection]]) between them, i.e. if there exists a [[Function (mathematics)|function]] from A to B such that for every [[Element (mathematics)|element]] y of B there is exactly one element x of A with f(x) = y.

== Description ==

Equinumerous finite sets have the same number of elements. The definition of equinumerosity using bijections can be applied to both finite and infinite sets and allows one to state whether two sets have the same size even if they are infinite.

Unlike finite sets, some infinite sets are equinumerous to proper subsets of themselves.

Equinumerous sets are said to have the same [[cardinality]].

== See also ==

* [[Cardinality]]
* [[Combinatorial class]]
* [[Hume's principle]]

== External links ==

* [https://en.wikipedia.org/wiki/Equinumerosity Equinumerosity]]

[[Category:Mathematics]]
[[Category:Set theory]]

Equinumerosity - Revision history

Karl Jones: Created page with "In mathematics, two sets A and B are '''equinumerous''' if there exists a one-to-one correspondence (a bijection) between them, i.e. if there exi..."