Definition:Signum Function

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

The signum function $\sgn: X \to \set {-1, 0, 1}$ is defined as:
 * $\forall x \in X: \map \sgn x := \sqbrk {x > 0} - \sqbrk {x < 0}$

where $\sqbrk {x > 0}$ etc. denotes Iverson's convention.

That is:
 * $\forall x \in X: \map \sgn x := \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.

Hence it can also be seen denoted as $\map {\mathrm {sign} } x$.

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