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Equivalence relation
Definition
$X$ |
$ \sim \in \text{EquivRel}(X) $ |
$ \sim \in \mathrm{Rel}(X) $ |
$x,y,z\in X$ |
$ x\sim x $ |
$ x\sim y \Leftrightarrow y\sim x $ |
$ x\sim y \land y\sim z \Leftrightarrow x\sim z $ |
Discussion
The relation $\sim$ is an equivalence relation, if it's in the intersection of all reflexive, all symmetric and all transitive relation. Hence
Reference
Wikipedia: Equivalence relation