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strict_partial_order [2013/09/04 17:24] nikolaj |
strict_partial_order [2014/03/21 11:11] |
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| - | ===== Strict partial order ===== | ||
| - | ==== Definition ==== | ||
| - | | @#88DDEE: $X$ | | ||
| - | | @#FFBB00: $ <\ \in\ \text{StrictPartOrd}(X) $ | | ||
| - | |||
| - | | @#88DDEE: $ R \in \mathrm{Rel}(X) $ | | ||
| - | | $ x,y,z\in X $ | | ||
| - | |||
| - | | @#55EE55: $ x \nless x $ | | ||
| - | | @#55EE55: $ x<y\land y<z \implies x<z $ | | ||
| - | |||
| - | Here we use infix notation: $x<y\ \equiv\ <(x,y)$. | ||
| - | |||
| - | ==== Discussion ==== | ||
| - | A strict partial order is automatically anti-symmetric. | ||
| - | === Reference === | ||
| - | Wikipedia: [[http://en.wikipedia.org/wiki/Order_relation|Order theory]], [[http://en.wikipedia.org/wiki/Poset|Poset]] | ||
| - | ==== Context ==== | ||
| - | === Subset of === | ||
| - | [[Reflexive relation]], [[Transitive relation]], [[Anti-symmetric relation]] | ||
