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monotonically_increasing_function [2014/02/17 20:34] nikolaj |
monotonically_increasing_function [2014/03/21 11:11] (current) |
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===== Monotonically increasing function ===== | ===== Monotonically increasing function ===== | ||
==== Function ==== | ==== 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 ==== |