Set of Natural Numbers is Primitive Recursive

Theorem
The set of natural numbers $\N$ is primitive recursive.

Proof
The characteristic function $\chi_\N: \N \to \N$ is defined as:
 * $\forall n \in \N: \chi_\N \left({n}\right) = 1$.

So:
 * $\chi_\N \left({n}\right) = f^1_1 \left({n}\right)$

The constant function $f^1_1$ is primitive recursive.

Hence the result.