Different natural numbers have different successors.
Zero is a natural number. Every natural number has a successor, which is also a natural number. Zero is not the successor of any natural number. Different natural numbers have different successors. And if zero has X, and each natural number relays X to its successor, then all natural numbers get X. These are statements of a group of statements of number theory published in 1889 by a mathematician who attributed them to Dedekind. FTP, give the collective name of these statements published by an Italian mathematician.
Zero is a natural number. Every natural number has a successor, which is also a natural number.
The 5 Peano Postulates or Peano Axioms