Why is $X^- = -\min\{X, 0\}$ ? This is how it is defined in a probability book I am self-studying.
For the function $X:\Omega \to \mathcal{R}$,
The positive part of $X$ is the function $X^+ = \max \{X, 0\}$.
The negative part of $X$ is the function $X^- = -\min \{X, 0\}$.
It seems to me that it should be: $X^- = \min\{X, 0\}$