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negative_part_of_a_function [2013/08/18 20:04] nikolaj created |
negative_part_of_a_function [2014/03/21 11:11] (current) |
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===== Negative part of a function ===== | ===== Negative part of a function ===== | ||
- | ==== Definition ==== | + | ==== Set ==== |
- | | @#88DDEE: $f:X\to Y$ | @#88DDEE: $(Y\subseteq \overline{\mathbb R})\land (0\in Y) $ | | + | | @#55CCEE: context | @#55CCEE: $f:X\to \overline{\mathbb R}$ | |
- | | @#55EE55: $ f^- $ | | + | | @#FFBB00: definiendum | @#FFBB00: $f^-:X\to \overline{\mathbb R}$ | |
+ | | @#FFBB00: definiendum | @#FFBB00: $ f^-(x) := \mathrm{max}(-f(x),0)$ | | ||
- | | @#88DDEE: $ f^-:X\to Y$ | | + | ==== Discussion ==== |
- | + | ||
- | | @#55EE55: $ f^-(x) := \mathrm{max}(-f(x),0)$ | | + | |
- | + | ||
- | ==== Ramifications ==== | + | |
- | === Discussion === | + | |
Notice that $f^-(x)\ge 0$. | Notice that $f^-(x)\ge 0$. | ||
- | ==== Context ==== | + | ==== Parents ==== |
- | === Parents === | + | === Context === |
[[Maximum function]], [[Extended real number line]] | [[Maximum function]], [[Extended real number line]] |