📂Functions

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 $\mathrm{sign}$.

See Also

• Sign of complex numbers