# Peano axioms

## Summary

The Peano axioms are a set of axioms, either in first- or second-order logic, for the system of natural numbers. The axioms define a successor operation and the principle of induction, and in some versions, addition, multiplication, and ordering as well. The Peano axioms serve as a formal model for number theory.

## Context

This concept has the prerequisites:

- first-order logic (The axioms can be stated in first-order logic.)

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## See also

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