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New Berkeley paradox in the theory of limits

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 aim is to reveal the return of the Berkeley paradox of the eighteenth century.

Design/methodology/approach

This is a conceptual discussion.

Findings

Since, long time ago, the common belief has been that the establishment and development of the theory of limits had provided an explanation for the Berkeley paradox. However, when the authors revisit some of the age‐old problems using the thinking logic of allowing both the concepts of potential and actual infinities, they find surprisingly that the shadow of the Berkeley paradox does not truly disappear in the foundation of mathematical analysis.

Originality/value

Show the incompleteness of the theory of limits, which is not the same as what has been believed in the history of mathematics.

Keywords

Citation

Zhu, W., Lin, Y., Gong, N. and Du, G. (2008), "New Berkeley paradox in the theory of limits", Kybernetes, Vol. 37 No. 3/4, pp. 474-481. https://doi.org/10.1108/03684920810863453

Publisher

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Emerald Group Publishing Limited

Copyright © 2008, Emerald Group Publishing Limited