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equivalence_relation [2007/03/30 20:45]
vkuncak
equivalence_relation [2007/03/30 20:45] (current)
vkuncak
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   * $x \sim y\ \land\ y \sim z\ \rightarrow\ x \sim z$   * $x \sim y\ \land\ y \sim z\ \rightarrow\ x \sim z$
  
-Given an equivalence relation $\sim$, we define the set of equivalence classes $A_{\sim}$ by+Given an equivalence relation $\sim$, we define the set of equivalence classes $A_{/\sim}$ by
 \begin{equation*} \begin{equation*}
-  A_{\sim} = \{ \{y \mid x \sim y\} \mid x \in A \}+  A_{/\sim} = \{ \{y \mid x \sim y\} \mid x \in A \}
 \end{equation*} \end{equation*}
  
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   x \sim y\ \iff\ \exists S \in P. \{x,y\} \subseteq S   x \sim y\ \iff\ \exists S \in P. \{x,y\} \subseteq S
 \end{equation*} \end{equation*}
-is an equivalence relation such that $A_{\sim} = P$.+is an equivalence relation such that $A_{/\sim} = P$.
  
 
equivalence_relation.txt · Last modified: 2007/03/30 20:45 by vkuncak
 
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