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. 1 has the property Q
    2. if x has property Q then x has property Q
  • then the property Q holds for all natural numbers.
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