# Definition:Signum Function/Signum Complement

## Definition

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 known as

Informally, as an obvious derivation of the notation, used, $\overline \sgn$ is often referred to as signum bar.

However, googling for signum bar is likely to lead you to an Italian eatery.