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Mathematical system of potential infinities (I) – preparation

Wujia Zhu (Department of Computer Science, Nanjing University of Aeronautics and Astronautics, Nanjing, People's Republic of China)
Yi Lin (School 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

Abstract

Purpose

Aims to focus on the co‐existence of potential and actual infinities in modern mathematics and its theoretical foundation. It has been shown that not only the whole system of modern mathematics but also the subsystems directly dealing with infinities have permitted the co‐existence of these two kinds of infinities.

Design/methodology/approach

The paper discusses the issues surrounding the two problems that urgently need to be solved. One of the problems is how to select an appropriate theoretical foundation for modern mathematics and the theory of computer science. The other problem is, under what interpretation can modern mathematics and the theory of computer science be kept in their entirety?

Findings

This paper constructs the mathematical system of potential infinities in an effort to address the two afore‐mentioned problems.

Originality/value

Highlights that the said mathematical system of potential infinities is completely different of the mathematical system constructed on the basis of intuitionism.

Keywords

Citation

Zhu, W., Lin, Y., Du, G. and Gong, N. (2008), "Mathematical system of potential infinities (I) – preparation", Kybernetes, Vol. 37 No. 3/4, pp. 489-493. https://doi.org/10.1108/03684920810863471

Publisher

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Emerald Group Publishing Limited

Copyright © 2008, Emerald Group Publishing Limited