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Cauchy theater phenomenon in diagonal method and test principle of finite positional differences

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)
Ningsheng Gong (College of Information Science, Nanjing University of Technology, Nanjing, People's Republic of China)
Guoping Du (Institute of Modern Logic and Applications, Nanjing University, Nanjing, People's Republic of China)

Kybernetes

ISSN: 0368-492X

Article publication date: 11 April 2008

Abstract

Purpose

The paper's purpose is to show a class of well‐used methods in set theory is invalid.

Design/methodology/approach

A conceptual approach is taken.

Findings

Based on the concept of Cauchy theater introduced elsewhere, it is proven that the argument employing the diagonal method for the fact that the set of all real numbers R={x|r(x)}, where r(x)=dfx is a real number” has an uncountable cardinality, is not valid. The diagonal method has appeared in naive and modern axiomatic set theories.

Originality/value

Point out more paradoxes in the methodology of mathematics.

Keywords

Citation

Zhu, W., Lin, Y., Gong, N. and Du, G. (2008), "Cauchy theater phenomenon in diagonal method and test principle of finite positional differences", Kybernetes, Vol. 37 No. 3/4, pp. 469-473. https://doi.org/10.1108/03684920810863444

Publisher

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Emerald Group Publishing Limited

Copyright © 2008, Emerald Group Publishing Limited