Definition:Signum Function/Signum Complement

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

The signum complement function $\overline {\operatorname{sgn}}: \N \to \left\{ {0, 1}\right\}$ is defined as:
 * $\forall n \in \N: \overline {\operatorname{sgn}} \left({n}\right) = \begin{cases}

1 & : n = 0 \\ 0 & : n > 0 \end{cases}$

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

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

Also see

 * Signum Complement Function on Natural Numbers as Characteristic Function