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Last updated: Mon Dec 1 2008

Created, developed, and nurtured by Eric Weisstein
at Wolfram Research
Foundations of Mathematics > Axioms >
Interactive Entries > Interactive Demonstrations >

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

REFERENCES:

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




CITE THIS AS:

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

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