Cannot understand the proof

Question

I was studying the proof for absolute convergence test. I could not understand the following expression while reading it. Could you, please, explain what this means? $$ x_+ = \max\{x, 0\},\qquad x_− = \max\{−x, 0\} $$

Answer 1

It means that$$x_+=\begin{cases}x&\text{ if }x>0\\0&\text{ otherwise}\end{cases}\text{ and that }x_-=\begin{cases}-x&\text{ if }-x>0\ (\iff x<0)\\0&\text{ otherwise.}\end{cases}$$