Peano axioms

In mathematics, the Peano axioms (or Peano postulates) are a set of first-order axioms proposed by Giuseppe Peano which determine the theory of Peano arithmetic (also known as first-order arithmetic). This theory constitutes a fundamental formalism for arithmetic, and the Peano axioms form a basis for the formalisation of stronger theories, such as second-order arithmetic.

Related Topics:
Mathematics - First-order - Axiom - Giuseppe Peano - Arithmetic - Second-order arithmetic

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Using the Peano axioms, one can construct many of the most important number systems and structures of modern mathematics. Peano arithmetic raises a number of metamathematical and philosophical issues, primarily involving questions of consistency and completeness.

Related Topics:
Number system - Metamathematical - Philosophical - Consistency - Completeness

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