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order-reflecting_function [2013/09/04 17:17] nikolaj |
order-reflecting_function [2014/03/21 11:11] (current) |
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| ===== Order-reflecting function ===== | ===== Order-reflecting function ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | $X,Y,\le_X,\le_Y$ | | + | | @#55CCEE: context | @#55CCEE: $X,Y$ | |
| - | | $ \le_X \in\text{NSPartialOrd}(X),\le_Y \in\text{NSPartialOrd}(Y) $ | | + | | @#55CCEE: context | @#55CCEE: $ \le_X,\le_Y $ | @#55CCEE: context | @#55CCEE: ...non-strict partial order | |
| - | ^ $ \{f\} $ ^ | + | | @#FFBB00: definiendum | @#FFBB00: $ f\in\mathrm{it} $ | |
| - | |$f:X\to Y$| | + | | $f:X\to Y$ | |
| - | |$x,y\in X$| | + | | $x,y\in X$ | |
| - | ^ $ \forall x,y\ ((f(x)\le_Y f(y)\implies x\le_X y)) $ ^ | + | | @#55EE55: postulate | @#55EE55: $ f(x)\le_Y f(y)\implies x\le_X y $ | |
| - | ==== Ramifications ==== | + | ==== Discussion ==== |
| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Monotone_function|Monotone function]] | Wikipedia: [[http://en.wikipedia.org/wiki/Monotone_function|Monotone function]] | ||
| - | ==== Context ==== | + | ==== Parents ==== |
| - | Function constructor | + | |
| === Refinement of === | === Refinement of === | ||
| [[Function]] | [[Function]] | ||
| - | === Parents === | + | === Context === |
| - | [[Order relation]] | + | [[Non-strict partial order]] |
