# Question about positive and negative parts $f^+ = \frac{|f| + f}{2}, f^- = \frac{|f| - f}{2}$

For an extended real-valued function $$f$$, do we have the representation $$\displaystyle f^+ = \frac{|f| + f}{2}$$ and $$\displaystyle f^- = \frac{|f| - f}{2}$$? At least it seems to say so on the Wikipedia page. But doesn't this not make sense if say $$f$$ is $$+\infty$$ or $$-\infty$$? E.g. if $$f$$ is $$-\infty$$ then then the numerator of $$f^+$$ is $$+\infty - \infty$$ which is undefined. And similary if $$f$$ is $$+\infty$$ then the numerator of $$f^-$$ is undefined.

• Your observation is correct. We cannot write $f^{+}=\frac {|f|+f} 2$ for extended real valued functions. – Kavi Rama Murthy Jun 30 at 5:17