Positive and negative parts of a function

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Definition

We define the positive and negative parts of a function as follows:

• [ilmath]f^+:=\max(f,0)[/ilmath] defined pointwise, so [ilmath]f^+(x)=\max(f(x),0)[/ilmath]
• [ilmath]f^-:=-\min(f,0)[/ilmath] defined pointwise, so [ilmath]f^-(x)=-\min(f(x),0)[/ilmath]

Then:

• [ilmath]f=f^+-f^-[/ilmath]