Definition: 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.