Lukas' Notes

number-theory

Definition

Peano Axioms

The Peano axioms are axioms for the natural numbers:

  1. 0 (zero) is a natural number.
  2. Every natural number has exactly one successor.
  3. 0 is not the successor of any natural number.
  4. Different natural numbers have different successors.
  5. Any property that applies to 0 and transfers from each natural number to its successor applies to all natural numbers.