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Peano axioms

The arithmetic ofPeano defines the natural numbers.



Peano's axioms contain the notion of a set. They define the (non-negative) integers as:

  1 0 is a natural number
  2 Every integer has a unique successor.
  3 There is an integer which is not a successor of any integer.
  4 Two distict integers cannot have the same successor.
  5 If M is a set of integers such that 0 is in M and such that if an integer n is in M then its successor is in M, then every integer is in M.


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