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strict_partial_order [2013/09/04 17:26] nikolaj |
strict_partial_order [2014/03/21 11:11] (current) |
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===== Strict partial order ===== | ===== Strict partial order ===== | ||
- | ==== Definition ==== | + | ==== Set ==== |
- | | @#88DDEE: $X$ | | + | | @#55CCEE: context | @#55CCEE: $X$ | |
- | | @#FFBB00: $ <\ \in\ \text{StrictPartOrd}(X) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ <\ \in\ \text{StrictPartOrd}(X) $ | |
- | | @#88DDEE: $ <\ \in\ \mathrm{Rel}(X) $ | | + | | @#55CCEE: context | @#55CCEE: $ <\ \in\ \mathrm{Rel}(X) $ | |
| $ x,y,z\in X $ | | | $ x,y,z\in X $ | | ||
- | | @#55EE55: $ x \nless x $ | | + | | @#55EE55: postulate | @#55EE55: $ x \nless x $ | |
- | | @#55EE55: $ x<y\land y<z \implies x<z $ | | + | | @#55EE55: postulate | @#55EE55: $ x<y\land y<z \implies x<z $ | |
Here we use infix notation: $x<y\ \equiv\ <(x,y)$. | Here we use infix notation: $x<y\ \equiv\ <(x,y)$. | ||
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=== Reference === | === Reference === | ||
Wikipedia: [[http://en.wikipedia.org/wiki/Order_relation|Order theory]], [[http://en.wikipedia.org/wiki/Poset|Poset]] | Wikipedia: [[http://en.wikipedia.org/wiki/Order_relation|Order theory]], [[http://en.wikipedia.org/wiki/Poset|Poset]] | ||
- | ==== Context ==== | + | ==== Parents ==== |
=== Subset of === | === Subset of === | ||
[[Reflexive relation]], [[Transitive relation]], [[Anti-symmetric relation]] | [[Reflexive relation]], [[Transitive relation]], [[Anti-symmetric relation]] |