Peano Axioms

Peano Axiom 1: 1 is a natural number.
Peano Axiom 2: Every natural number n has a unique successor S(n), which is also a natural number.
Peano Axiom 3: 1 is not the successor of any natural number.
Peano Axiom 4: If m and n are natural numbers and \(m \neq n\), then \(S(m)\neq S(n)\).