# Differences

This shows you the differences between two versions of the page.

equivalence_relation [2013/09/02 23:18] nikolaj |
equivalence_relation [2014/03/21 11:11] |
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- | ===== Equivalence relation ===== | ||

- | ==== Definition ==== | ||

- | | @#88DDEE: $X$ | | ||

- | | @#FFBB00: $ \sim \in \text{EquivRel}(X) $ | | ||

- | |||

- | | $x,y,z\in X$ | | ||

- | |||

- | | @#55EE55: $ \forall (u\in \text{dom}(\sim)).\ u\sim u $ | | ||

- | | @#55EE55: $ x\sim y \Leftrightarrow y\sim x $ | | ||

- | | @#55EE55: $ x\sim y \land y\sim z \Leftrightarrow x\sim z $ | | ||

- | |||

- | ==== Discussion ==== | ||

- | The relation $R$ is an equivalence relation, if it's in the intersection of all reflexive, all symmetric and all transitive relation. Hence | ||

- | === Reference === | ||

- | Wikipedia: [[http://en.wikipedia.org/wiki/Equivalence_relation|Equivalence relation]] | ||

- | ==== Context ==== | ||

- | === Subset of === | ||

- | [[Reflexive relation]], [[Symmetric relation]], [[Transitive relation]] |