Zero is not a successor

Statement

Let $S \colon \mathbb{N} \to \mathbb{N}$ be the successor function of the natural numbers. For each natural number $n$, $S(n) \neq 0$.

Remarks

This is one of the Peano axioms. In a construction of $\mathbb{N}$, it is a theorem. With the injectivity of the successor function, it shows that the numbers $0, S(0), S(S(0)), \dots$ are all different.

Explanations

L1 human

When you count up from any natural number, you never get back to $0$. Thus the natural numbers do not go around in a circle, like the hours on a clock do.