Definition:Non-Successor Element

Definition
Let $\left({P, s, 0}\right)$ be a Peano structure.

Then the element $0 \in P$ is called the non-successor element.

This is justified by Axiom $(P4)$, which stipulates that $0$ is not in the image of the successor mapping $s$.

Also known as
It would be nice if there were a name for this element more terse than non-successor element and more general than zero.

A suggestion coined at is primal element.