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The inconsistency of countable infinite sets

Wujia Zhu (Department of Computer Science, Nanjing University of Aeronautics and Astronautics, Nanjing, People's Republic of China)
Yi Lin (College 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)

Kybernetes

ISSN: 0368-492X

Article publication date: 11 April 2008

Abstract

Purpose

The paper aims to show countable infinite sets are self‐contradictory non‐sets.

Design/methodology/approach

The paper is a conceptual discussion.

Findings

Since, long ago, it has been commonly believed that the establishment and development of modern axiomatic set theory have provided a method to explain Russell's paradox. On the other hand, even though it has not been proven theoretically that there will not appear new paradoxes in modern axiomatic set theory, it has been indeed a century that no one has found a new paradox in modern axiomatic set theory. However, when we revisit some well‐known results and problems under the thinking logic of allowing two kinds of infinities, we discover that various countable infinite sets, widely studied and employed in modern axiomatic set theory, are all specious non‐sets.

Originality/value

A well‐known concept is shown to be not as correct as what has been believed.

Keywords

Citation

Zhu, W., Lin, Y., Du, G. and Gong, N. (2008), "The inconsistency of countable infinite sets", Kybernetes, Vol. 37 No. 3/4, pp. 446-452. https://doi.org/10.1108/03684920810863408

Publisher

:

Emerald Group Publishing Limited

Copyright © 2008, Emerald Group Publishing Limited