Set of Natural Numbers is Primitive Recursive

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

Proof
The characteristic function of $$\chi_{\N}: \N \to \N$$ 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.