This is an old revision of the document!


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

Context

Subset of

Link to graph
Log In
Improvements of the human condition