TOPICS
Search

Peano's Axioms


1. Zero is a number.

2. If a is a number, the successor of a 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 S of numbers contains zero and also the successor of every number in S, then every number is in S.

Peano's axioms are the basis for the version of number theory known as Peano arithmetic.


See also

Induction Axiom, Peano Arithmetic

Explore with Wolfram|Alpha

WolframAlpha

More things to try:

References

Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, p. 1152, 2002.

Referenced on Wolfram|Alpha

Peano's Axioms

Cite this as:

Weisstein, Eric W. "Peano's Axioms." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PeanosAxioms.html

Subject classifications