Definition:Signum Function/Natural Numbers

Definition

The signum function $\sgn: \N \to \set {0, 1}$ is the restriction of the signum function to the natural numbers, defined as:

$\forall n \in \N: \map \sgn n := \begin {cases} 0 & : n = 0 \\ 1 & : n > 0 \end{cases}$

Signum Complement

Let $\sgn: \N \to \set {0, 1}$ be the signum function on the natural numbers.

The signum complement function $\overline \sgn: \N \to \set {0, 1}$ is defined as:

$\forall n \in \N: \map {\overline \sgn} n := \begin {cases} 1 & : n = 0 \\ 0 & : n > 0 \end {cases}$

Also see

• Signum Function on Natural Numbers as Characteristic Function