Nonzero natural number has successor

Let $\N$ be the 0-based natural numbers:
$\N = \left\{{0, 1, 2, \ldots}\right\}$
Let $s: \N \to \N: \map s n = n + 1$ be the successor function.
$\forall n \in \N \setminus \set 0 \left( \exists m \in \N: \map s m = n\right)$