The inconsistency of the natural number system
Wujia Zhu
(Department of Computer Science, Nanjing University of Aeronautics and Astronautics, Nanjing, People's Republic of China)
Yi Lin
(School of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, People's Republic of China Department of Mathematics, Slippery Rock University, Slippery Rock, Pennsylvania, USA)
Guoping Du
(Institute of Modern Logic and Applications, Nanjing University, Nanjing, People's Republic of China)
Ningsheng Gong
(College of Information Science, Nanjing University of Technology, Nanjing, People's Republic of China)
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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.
Keywords
Citation
Zhu, W., Lin, Y., Du, G. and Gong, N. (2008), "The inconsistency of the natural number system", Kybernetes, Vol. 37 No. 3/4, pp. 482-488. https://doi.org/10.1108/03684920810863462
Publisher
:Emerald Group Publishing Limited
Copyright © 2008, Emerald Group Publishing Limited