Peano's axioms are the basis for the version of Number Theory known as Peano Arithmetic.
- 1. Zero is a number.
- 2. If is a number, the successor of is a number.
- 3. Zero is not the successor of a number.
- 4. Two numbers of which the successors are equal are themselves equal.
- 5. (Induction Axiom.) If a set of numbers contains Zero and also the successor of every number in
, then every number is in .
See also Induction Axiom, Peano Arithmetic
© 1996-9 Eric W. Weisstein