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anti-symmetric_relation [2013/08/15 12:15] ben |
anti-symmetric_relation [2013/09/02 18:57] nikolaj |
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| ===== Anti-symmetric relation ===== | ===== Anti-symmetric relation ===== | ||
| ==== Definition ==== | ==== Definition ==== | ||
| - | | $X$ | | + | | @#88DDEE: $X$ | |
| - | | $ R\in\text{Rel}(X) $ | | + | |
| - | ^ $ \{R\} $ ^ | + | | @#FFBB00: $ R\in\mathrm{SymmetricRel}(X) $ | |
| - | ^ $ (\langle x,y\rangle \in R) \land (\langle y,x\rangle \in R) \implies (x=y) $ ^ | + | | $ x,y\in X $ | |
| - | ==== Ramifications ==== | + | | @#55EE55: $ xRy \land yRx \implies x=y $ | |
| + | |||
| + | ==== Discussion ==== | ||
| + | === 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 ==== | ==== Context ==== | ||
| === Subset of === | === Subset of === | ||
| [[Binary relation on a set]] | [[Binary relation on a set]] | ||
| - | |||
