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Problem of infinity between predicates and infinite sets

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)
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

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Abstract

Purpose

The paper's aim is to reconsider the feasibility at both the heights of mathematics and philosophy of the statement that each predicate determines a unique set.

Design/methodology/approach

A conceptual approach is taken.

Findings

In the naive and the modern axiomatic set theories, it is a well‐known fact that each predicate determines precisely one set. That is to say, for any precisely defined predicate P, there is always A={x|P(x)} or xAP(x). However, when the authors are influenced by the thinking logic of allowing both kinds of infinities and compare these two kinds of infinities, and potentially infinite and actually infinite intervals and number sets, it is found that the expressions of these number sets are not completely reasonable.

Originality/value

Detailed analyses are given for the introduction of new symbols and representations for either potential or actual infinite sets.

Keywords

Citation

Zhu, W., Lin, Y., Gong, N. and Du, G. (2008), "Problem of infinity between predicates and infinite sets", Kybernetes, Vol. 37 No. 3/4, pp. 526-533. https://doi.org/10.1108/03684920810863516

Publisher

:

Emerald Group Publishing Limited

Copyright © 2008, Emerald Group Publishing Limited