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2014•Mathematical theory and modelingRequires access

An Extension of Peano Axioms for the Natural Number System

Stephen Sebastine Akpan, John Usen, T. A. Ugbe

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Abstract

As a fundamental requirement, a natural number system must necessarily satisfy   Peano axioms. These axioms altogether justify whether or not a number system is a natural number system. In this paper, a set of axioms have been proposed and established to augment and extend the existing Peano axioms for the natural number system. Key Words: Natural numbers, Rational numbers, Peano axioms, Pearson   correlation  coefficient, Even and Odd partitions.

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What this paper is about

As a fundamental requirement, a natural number system must necessarily satisfy   Peano axioms. These axioms altogether justify whether or not a number system is a natural number system. In this paper, a set of axioms have been proposed and established to augment and extend the existing Peano axioms for the natural number system. Key Words: Natural numbers, Rational numbers, Peano axioms, Pearson   correlation  coefficient, Even and Odd partitions.

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Available abstract

As a fundamental requirement, a natural number system must necessarily satisfy   Peano axioms. These axioms altogether justify whether or not a number system is a natural number system. In this paper, a set of axioms have been proposed and established to augment and extend the existing Peano axioms for the natural number system. Key Words: Natural numbers, Rational numbers, Peano axioms, Pearson   correlation  coefficient, Even and Odd partitions.

Key concepts: Peano axioms, Axiom, Mathematics, Extension (predicate logic), Axiomatic system, Natural number, Natural (archaeology), Set (abstract data type)

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