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.
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