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The inconsistency of the natural number system

The inconsistency of the natural number system Purpose – The paper aims to use a third method to show that the system of natural numbers is inconsistent. Design/methodology/approach – A conceptual approach is taken. Findings – Without directly employing the concepts of potential and actual infinities, the authors show that the concept of the set N ={ x | n ( x )}, where n ( x )= def “ x is a natural number” of all natural numbers is a self‐contradicting, incorrect concept. Originality/value – The paper shows the system of natural numbers to be inconsistent. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Kybernetes Emerald Publishing

The inconsistency of the natural number system

Kybernetes , Volume 37 (3/4): 7 – Apr 11, 2008

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Publisher
Emerald Publishing
Copyright
Copyright © 2008 Emerald Group Publishing Limited. All rights reserved.
ISSN
0368-492X
DOI
10.1108/03684920810863462
Publisher site
See Article on Publisher Site

Abstract

Purpose – The paper aims to use a third method to show that the system of natural numbers is inconsistent. Design/methodology/approach – A conceptual approach is taken. Findings – Without directly employing the concepts of potential and actual infinities, the authors show that the concept of the set N ={ x | n ( x )}, where n ( x )= def “ x is a natural number” of all natural numbers is a self‐contradicting, incorrect concept. Originality/value – The paper shows the system of natural numbers to be inconsistent.

Journal

KybernetesEmerald Publishing

Published: Apr 11, 2008

Keywords: Cybernetics; Set theory; Mathematics; Number theory

References