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Descriptive definitions of potential and actual infinities

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 analyze the concepts of potential and actual infinities.

Design/methodology/approach

The exploration and research on potential and actual infinities generally touch on many disciplines, such as philosophy, logic, computer science, mathematics, etc. From the angle of a brief history, recall and development, the authors analyze the concepts of potential and actual infinities on one starting point and two locations to cut in.

Findings

Clarify the difference and connection of these two infinities on the level of mathematics and introduce the symbolized, descriptive definitions for potential and actual infinities.

Originality/value

It is the first time that the difference between the concepts of potential and actual infinities are clarified, which leads to the discovery of the fourth crisis in the foundations of mathematics.

Keywords

Citation

Zhu, W., Lin, Y., Gong, N. and Du, G. (2008), "Descriptive definitions of potential and actual infinities", Kybernetes, Vol. 37 No. 3/4, pp. 424-432. https://doi.org/10.1108/03684920810863372

Publisher

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Emerald Group Publishing Limited

Copyright © 2008, Emerald Group Publishing Limited