1.4. Natural Numbers, Integers, and Rational Numbers
Definition 1.4.1: Peano Axioms
- 1 is a natural number
- For every natural number x there exists another natural number x’ called the successor of x.
- 1 # x’ for every natural number x (x’ being the successor of x)
- If x’ = y’ then x = y
- If Q is a property such that:
- 1 has the property Q
- if x has property Q then x’ has property Q
- then the property Q holds for all natural numbers.