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Modern system of mathematics and special Cauchy theater in its theoretical foundation

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, Polytechnic University, Nanjing, People's Republic of China)

Kybernetes

ISSN: 0368-492X

Article publication date: 11 April 2008

Abstract

Purpose

The paper aims to employ a different approach to show that the countable infinite sets are self‐contradictory non‐sets.

Design/methodology/approach

The paper discusses the concept.

Findings

The concept of infinities in the countable set theory was discussed in Zhu et al. by employing the method of analysis of allowing two different kinds of infinities. What was obtained is that various countable infinite sets, studied in the naïve and modern axiomatic set theories, are all incorrect concepts containing self‐contradictions. In this paper, the authors provide another argument to prove the same conclusion: various countable infinite sets studied in both naïve and modern axiomatic set theories are all specious non‐sets. The argument is given from a different angle on still the same premise of allowing two different concepts of infinities.

Originality/value

The concept of Cauchy theater is introduced.

Keywords

Citation

Zhu, W., Lin, Y., Du, G. and Gong, N. (2008), "Modern system of mathematics and special Cauchy theater in its theoretical foundation", Kybernetes, Vol. 37 No. 3/4, pp. 458-464. https://doi.org/10.1108/03684920810863426

Publisher

:

Emerald Group Publishing Limited

Copyright © 2008, Emerald Group Publishing Limited