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anti-symmetric_relation [2013/09/04 17:23] nikolaj |
anti-symmetric_relation [2014/03/21 11:11] (current) |
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| ===== Anti-symmetric relation ===== | ===== Anti-symmetric relation ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $X$ | | + | | @#55CCEE: context | @#55CCEE: $X$ | |
| - | | @#FFBB00: $ R\in\mathrm{SymmetricRel}(X) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ R\in\mathrm{SymmetricRel}(X) $ | |
| - | | @#88DDEE: $ R \in \mathrm{Rel}(X) $ | | + | | @#55CCEE: context | @#55CCEE: $ R \in \mathrm{Rel}(X) $ | |
| | $ x,y\in X $ | | | $ x,y\in X $ | | ||
| - | | @#55EE55: $ xRy \land yRx \implies x=y $ | | + | | @#55EE55: postulate | @#55EE55: $ xRy \land yRx \implies x=y $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Anti-symmetric_relation|Anti-symmetric relation]] | Wikipedia: [[http://en.wikipedia.org/wiki/Anti-symmetric_relation|Anti-symmetric relation]] | ||
| - | ==== Context ==== | + | ==== Parents ==== |
| === Subset of === | === Subset of === | ||
| [[Binary relation on a set]] | [[Binary relation on a set]] | ||
