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

Modern system of mathematics and special Cauchy theater in its theoretical foundation 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Kybernetes Emerald Publishing

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

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

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References (8)

Publisher
Emerald Publishing
Copyright
Copyright © 2008 Emerald Group Publishing Limited. All rights reserved.
ISSN
0368-492X
DOI
10.1108/03684920810863426
Publisher site
See Article on Publisher Site

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.

Journal

KybernetesEmerald Publishing

Published: Apr 11, 2008

Keywords: Cybernetics; Set theory

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