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

Cauchy theater phenomenon in diagonal method and test principle of finite positional differences 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 )= df “ x 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Kybernetes Emerald Publishing

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

Kybernetes , Volume 37 (3/4): 5 – Apr 11, 2008

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Publisher
Emerald Publishing
Copyright
Copyright © 2008 Emerald Group Publishing Limited. All rights reserved.
ISSN
0368-492X
DOI
10.1108/03684920810863444
Publisher site
See Article on Publisher Site

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 )= df “ x 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.

Journal

KybernetesEmerald Publishing

Published: Apr 11, 2008

Keywords: Cybernetics; Set theory

References