# Differences

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 negative_part_of_a_function [2013/08/18 20:04]nikolaj created negative_part_of_a_function [2013/09/06 01:48]nikolaj 2013/09/06 01:48 nikolaj 2013/09/06 01:48 nikolaj 2013/08/18 20:04 nikolaj created Next revision Previous revision 2013/09/06 01:48 nikolaj 2013/09/06 01:48 nikolaj 2013/08/18 20:04 nikolaj created Line 1: Line 1: ===== Negative part of a function ===== ===== Negative part of a function ===== ==== Definition ==== ==== Definition ==== - | @#88DDEE: $f:​X\to ​Y$ | @#88DDEE: $(Y\subseteq ​\overline{\mathbb R})\land (0\in Y)$ | + | @#88DDEE: $f:X\to \overline{\mathbb R}$ | - | @#55EE55: $f^-$ | + | @#FFBB00: $f^-:X\to \overline{\mathbb R}$ | + | @#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 ==== ==== Context ==== - === Parents ​=== + === Requirements ​=== [[Maximum function]], [[Extended real number line]] [[Maximum function]], [[Extended real number line]]