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.

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

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