Synopsis:
 Axiomatization of the mathematical theory of natural numbers:
 1. Zero is a natural number.
 2. Zero is not the successor of any natural number.
 3. Every natural number has a successor, which is a natural number.
 4. If the successor of natural number a is equal to the successor of natural number b, then a and b are equal.
 5. Suppose:
 (i) zero has a property P;
 (ii) if every natural number less than a has the property P then a also has the property P.
 Then every natural number has the property P.
