• 0 is a natural number
• Every natural number n has a successor s(n), which is also a natural number. (You can think of the successor of a number n as n+1.)
• For every natural number n the successor s(n) is not equal to 0.
• If for any two natural numbers m and n we have s(m)=s(n), then m=n.
• The final axiom concerns the method of induction, described at the end of this article