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quotient_set [2013/05/23 17:26] nikolaj created |
quotient_set [2014/03/21 11:11] 127.0.0.1 external edit |
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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) $ | |
- | ^ $ Y\in X/\sim $ ^ | + | | @#FFBB00: definiendum | @#FFBB00: $ Y\in X/\sim $ | |
- | | $x\in X$ | | + | | @#55EE55: postulate | @#55EE55: $ \exists x.\ Y=[x]_\sim $ | |
- | ^ $ \exists x\ (Y=[x]_\sim) $ ^ | + | ==== Discussion ==== |
- | + | ||
- | ==== 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 ==== |
- | === Parents === | + | === Context === |
[[Equivalence class]] | [[Equivalence class]] |