\begin{definition}[Definition:Signum Function/Natural Numbers]
The '''signum function''' $\sgn: \N \to \set {0, 1}$ is the restriction of the signum function to the natural numbers, defined as:
:$\forall n \in \N: \map \sgn n := \begin{cases}
0 & : n = 0 \\
1 & : n > 0
\end{cases}$
\end{definition}