Definition:Signum Function

Definition
Let $X \subseteq \R$ be a subset of the real numbers.

The signum function $\operatorname{sgn}: X \to \left\{ {-1, 0, 1}\right\}$ is defined as:
 * $\forall x \in X: \operatorname{sgn} \left({x}\right) = \left[{x > 0}\right] - \left[{x < 0}\right]$

where $\left[{x > 0}\right]$ etc. denotes Iverson's convention.

That is:
 * $\forall x \in X: \operatorname{sgn} \left({x}\right) = \begin{cases}

-1 & : x < 0 \\ 0 & : x = 0 \\ 1 & : x > 0 \end{cases}$

Also known as
The signum of a number is known, informally and colloquially, as its sign.

It is also seen denoted as $\operatorname{sign} \left({x}\right)$.

The concept of a number as being signed or unsigned is used in computer science to distinguish between integers and natural numbers.

Also see

 * Definition:Sign of Number
 * Definition:Sign of Permutation


 * Signum Function on Integers is Extension of Signum on Natural Numbers