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 equivalence_relation [2013/09/02 23:18]nikolaj equivalence_relation [2014/03/21 11:11] Line 1: Line 1: - ===== 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]]