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quotient_set [2013/05/23 17:26] nikolaj created |
quotient_set [2014/12/27 00:17] nikolaj |
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| ===== Quotient set ===== | ===== Quotient set ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | $X,\sim$ | | + | | @#55CCEE: context | @#55CCEE: $X$ | |
| - | | $ \sim\in\text{Equiv}(X) $ | | + | | @#55CCEE: context | @#55CCEE: $ \sim\in\text{Equiv}(X) $ | |
| + | | @#FFBB00: definiendum | @#FFBB00: $ Y\in X/\sim $ | | ||
| + | | @#55EE55: postulate | @#55EE55: $ \exists x.\ Y=[x]_\sim $ | | ||
| - | ^ $ Y\in X/\sim $ ^ | + | ----- |
| - | + | ||
| - | | $x\in X$ | | + | |
| - | + | ||
| - | ^ $ \exists x\ (Y=[x]_\sim) $ ^ | + | |
| - | + | ||
| - | ==== Ramifications ==== | + | |
| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Equivalence_class|Equivalence class]] | Wikipedia: [[http://en.wikipedia.org/wiki/Equivalence_class|Equivalence class]] | ||
| - | ==== Context ==== | + | |
| - | === Parents === | + | ----- |
| + | === Context === | ||
| [[Equivalence class]] | [[Equivalence class]] | ||
