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equivalence_relation [2013/09/02 23:18]
nikolaj
equivalence_relation [2014/03/21 11:11] (current)
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 ===== Equivalence relation ===== ===== Equivalence relation =====
-==== Definition ​==== +==== Set ==== 
-| @#88DDEE: $X$ |+| @#55CCEE: context ​    | @#55CCEE: $X$ |
  
-| @#FFBB00: $ \sim \in \text{EquivRel}(X) $ |+| @#FFBB00: definiendum ​| @#FFBB00: $ \sim \in \text{EquivRel}(X) $ |
  
 +| @#55CCEE: context ​    | @#55CCEE: $ \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: postulate ​  | @#55EE55: $ x\sim $ | 
-| @#55EE55: $ x\sim y \Leftrightarrow y\sim x $ | +| @#55EE55: postulate ​  | @#55EE55: $ x\sim y \Leftrightarrow y\sim x $ | 
-| @#55EE55: $ x\sim y \land y\sim z \Leftrightarrow x\sim z $ |+| @#55EE55: postulate ​  | @#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]]
-==== Context ​====+==== Parents ​====
 === Subset of === === Subset of ===
 [[Reflexive relation]], [[Symmetric relation]], [[Transitive relation]] [[Reflexive relation]], [[Symmetric relation]], [[Transitive relation]]
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