\begin{definition}[Definition:Signum Function/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:
:$\forall n \in \N: \map {\overline \sgn} n := \begin{cases}
1 & : n = 0 \\
0 & : n > 0
\end{cases}$
\end{definition}