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equivalence_relation [2007/03/30 20:44] vkuncak |
equivalence_relation [2007/03/30 20:45] vkuncak |
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| 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 \} | ||
| \end{equation*} | \end{equation*} | ||