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 monotonically_increasing_function [2014/02/17 20:32]nikolaj monotonically_increasing_function [2014/03/21 11:11] (current) Both sides previous revision Previous revision 2014/02/17 20:34 nikolaj 2014/02/17 20:32 nikolaj 2014/02/13 16:13 external edit2013/09/07 22:55 nikolaj created Next revision Previous revision 2014/02/17 20:34 nikolaj 2014/02/17 20:32 nikolaj 2014/02/13 16:13 external edit2013/09/07 22:55 nikolaj created Line 1: Line 1: ===== 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: $f\in\mathrm{it}$ | - | @#AAFFAA: $f:X\to Y$ | + | @#AAFFAA: inclusion ​  | @#AAFFAA: $f:X\to Y$ | - | @#FFFDDD: $x,y\in X$ | + | @#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 ==== Line 18: Line 18: === Context === === Context === [[Non-strict partial order]] [[Non-strict partial order]] + === Related === + [[Monotonically decreasing function]]