The Five Peano Postulates

1. 1 is a positive integer.
2. Every positive integer has a unique positive integer as its successor.
3. No positive integer has 1 as its successor.
4. Distinct positive integers have different successors.
5. If a statement holds for the positive integer 1, and if, whenever it holds for a positive integer, it also holds for that integer's successor, then the statement holds for all positive integers.

The fifth postulate is the basis for the principle of mathematical induction.