# Definition:Signum Function/Signum Complement

< Definition:Signum Function(Redirected from Definition:Signum Complement)

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## 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.