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equivalence_class [2013/05/23 17:28] nikolaj |
equivalence_class [2014/08/23 18:22] nikolaj |
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| ===== Equivalence class ===== | ===== Equivalence class ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | $X,x,\sim$ | | + | | @#55CCEE: context | @#55CCEE: $X$ | |
| - | | $x\in X$ | | + | | @#55CCEE: context | @#55CCEE: $x\in X$ | |
| - | | $ \sim\in\text{Equiv}(X) $ | | + | | @#55CCEE: context | @#55CCEE: $\sim\in\text{Equiv}(X) $ | |
| - | + | | @#FFBB00: definiendum | @#FFBB00: $ y\in [x]_\sim $ | | |
| - | ^ $ y\in [x]_\sim $ ^ | + | | @#55EE55: postulate | @#55EE55: $y\sim x$ | |
| - | + | ||
| - | | $ y\in X $ | | + | |
| - | + | ||
| - | ^ $y\sim x$ ^ | + | |
| ==== Ramifications ==== | ==== Ramifications ==== | ||
| Line 16: | Line 12: | ||
| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Equivalence_class|Equivalence class]] | Wikipedia: [[http://en.wikipedia.org/wiki/Equivalence_class|Equivalence class]] | ||
| - | ==== Context ==== | + | ==== Parents ==== |
| - | === Parents === | + | === Context === |
| [[Equivalence relation]] | [[Equivalence relation]] | ||
