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Modern system of mathematics and general 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, Nanjing, People's Republic of China)

Kybernetes

ISSN: 0368-492X

Article publication date: 11 April 2008

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Abstract

Purpose

The paper aims to show using a different method that any uncountable set is a self‐contradictory non‐set.

Design/methodology/approach

The paper discusses the concept.

Findings

Elsewhere it is shown that in the framework of ZFC, various countable infinite sets are all self‐contradicting non‐sets. In this paper, the authors will generalize the concept of Cauchy theater, and establish the concept of transfinite Cauchy theaters. After that, employing a new method, they will prove that various uncountable infinite sets, as studied in naive set theory and modern axiomatic set theory, are also self‐contradicting non‐sets.

Originality/value

The concept of general Cauchy theater is introduced.

Keywords

Citation

Zhu, W., Lin, Y., Du, G. and Gong, N. (2008), "Modern system of mathematics and general Cauchy theater in its theoretical foundation", Kybernetes, Vol. 37 No. 3/4, pp. 465-468. https://doi.org/10.1108/03684920810863435

Publisher

:

Emerald Group Publishing Limited

Copyright © 2008, Emerald Group Publishing Limited