Category:Signum Function

This category contains results about Signum Function.
Definitions specific to this category can be found in Definitions/Signum Function.

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}$