Differences
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equivalence_relation [2013/09/02 23:18] nikolaj |
equivalence_relation [2013/09/04 17:27] nikolaj |
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| | @#FFBB00: $ \sim \in \text{EquivRel}(X) $ | | | @#FFBB00: $ \sim \in \text{EquivRel}(X) $ | | ||
| + | | @#88DDEE: $ \sim \in \mathrm{Rel}(X) $ | | ||
| | $x,y,z\in X$ | | | $x,y,z\in X$ | | ||
| - | | @#55EE55: $ \forall (u\in \text{dom}(\sim)).\ u\sim u $ | | + | | @#55EE55: $ x\sim x $ | |
| | @#55EE55: $ x\sim y \Leftrightarrow y\sim x $ | | | @#55EE55: $ x\sim y \Leftrightarrow y\sim x $ | | ||
| | @#55EE55: $ x\sim y \land y\sim z \Leftrightarrow x\sim z $ | | | @#55EE55: $ x\sim y \land y\sim z \Leftrightarrow x\sim z $ | | ||
| ==== Discussion ==== | ==== Discussion ==== | ||
| - | The relation $R$ is an equivalence relation, if it's in the intersection of all reflexive, all symmetric and all transitive relation. Hence | + | The relation $\sim$ is an equivalence relation, if it's in the intersection of all reflexive, all symmetric and all transitive relation. Hence |
| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Equivalence_relation|Equivalence relation]] | Wikipedia: [[http://en.wikipedia.org/wiki/Equivalence_relation|Equivalence relation]] | ||
