Axiom:Peano's Axioms/Also defined as

This template is to be used in "Also defined as" sections in pages discussing Peano's Axioms. Some treatments of this topic define the non-successor element (or primal element) to be $1$ and not $0$.

The treatments are similar, but the $1$-based system results in an algebraic structure which has no identity element for addition, and so no zero for multiplication.