# Peano's axioms for the Natural numbers

- 1 is a natural number.

- Every natural number $n$ has a natural number $n^\prime$ as a successor.

- 1 is not the successor of a natural number.

- Natural numbers with the same successor are the same.

- If the set $X$ contains 1 and for every natural number $n$ also its successor $n^\prime$, then the natural numbers form a subset of $X$.