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equivalence_relation [2013/09/04 17:27]
nikolaj
equivalence_relation [2014/03/21 11:11]
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-===== Equivalence relation ===== 
-==== Definition ==== 
-| @#88DDEE: $X$ | 
  
-| @#FFBB00: $ \sim \in \text{EquivRel}(X) $ | 
- 
-| @#88DDEE: $ \sim  \in \mathrm{Rel}(X) $ | 
-| $x,y,z\in X$ | 
- 
-| @#55EE55: $ x\sim x $ | 
-| @#55EE55: $ x\sim y \Leftrightarrow y\sim x $ | 
-| @#55EE55: $ 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: [[http://​en.wikipedia.org/​wiki/​Equivalence_relation|Equivalence relation]] 
-==== Context ==== 
-=== Subset of === 
-[[Reflexive relation]], [[Symmetric relation]], [[Transitive relation]] 
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