Sign function
Definition
Sign function $\mathrm{sgn} : \mathbb{R} \to \mathbb{R}$ is defined as follows.
$$ \mathrm{sgn}(x) :=\begin{cases} 1 & x>0 \\ 0 & x=0 \\ -1 & x<0 \end{cases} $$
Explanation
It is mainly used to simplify the notation of equations or definitions. It is also written as $\mathrm{sign}$.