Difference between revisions of "Equivalence relation"

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An equivalence relation is a special kind of relation

Given a relation $R$ in $A$ we require the following properties to define a relation (these are restated for convenience from the relation page)

A relation $R$ if for all $a\in A$ we have $aRa$

A relation $R$ is symmetric if for all $a,b\in A$ we have $aRb\implies bRa$

A relation $R$ is transitive if for all $a,b,c\in A$ we have $aRb\text{ and }bRc\implies aRc$

A relation $R$ is an equivalence relation if it is:

Revision as of 13:51, 6 March 2015 (view source) Alec (Talk \| contribs) (Created page with "An equivalence relation is a special kind of relation ==Required properties== Given a relation {{M\|R}} in {{M\|A}} we require the following properties to define a...")		Revision as of 13:17, 19 February 2016 (view source) Alec (Talk \| contribs) m Newer edit →
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	An equivalence relation is a special kind of [[Relation\|relation]]		An equivalence relation is a special kind of [[Relation\|relation]]