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monotonically_increasing_function [2014/02/13 16:13] 127.0.0.1 external edit |
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| ===== Monotonically increasing function ===== | ===== Monotonically increasing function ===== | ||
| - | ==== Set ==== | + | ==== Function ==== |
| - | | @#88DDEE: $X,Y$ | | + | | @#55CCEE: context | @#55CCEE: $ X,Y $ | |
| - | | @#88DDEE: $ \le_X,\le_Y $ ...non-strict partial order | | + | | @#55CCEE: context | @#55CCEE: $ \le_X,\le_Y $ ... non-strict partial order | |
| - | | @#FFBB00: $ f\in\mathrm{it} $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ f\in\mathrm{it} $ | |
| - | | @#55EE55: $f:X\to Y$ | | + | | @#AAFFAA: inclusion | @#AAFFAA: $f:X\to Y$ | |
| - | | $x,y\in X$ | | + | | @#FFFDDD: for all | @#FFFDDD: $x,y\in X$ | |
| - | | @#55EE55: $ x\le_X y \implies f(x)\le_Y f(y) $ | | + | | @#55EE55: postulate | @#55EE55: $ x\le_X y \implies f(x)\le_Y f(y) $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| - | === Reference === | ||
| - | Wikipedia: [[http://en.wikipedia.org/wiki/Monotone_function|Monotone function]] | ||
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Refinement of === | + | === Subset of === |
| [[Function]] | [[Function]] | ||
| === Context === | === Context === | ||
| [[Non-strict partial order]] | [[Non-strict partial order]] | ||
| + | === Related === | ||
| + | [[Monotonically decreasing function]] | ||
