To read the full version of this content please select one of the options below:

Inconsistency of uncountable infinite sets under ZFC framework

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)
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

Downloads
159

Abstract

Purpose

The purpose is to show that all uncountable infinite sets are self‐contradictory non‐sets.

Design/methodology/approach

A conceptual approach is taken in the paper.

Findings

Given the fact that the set N={x|n(x)} of all natural numbers, where n(x)=dfx is a natural number” is a self‐contradicting non‐set in this paper, the authors prove that in the framework of modern axiomatic set theory ZFC, various uncountable infinite sets are either non‐existent or self‐contradicting non‐sets. Therefore, it can be astonishingly concluded that in both the naive set theory or the modern axiomatic set theory, if any of the actual infinite sets exists, it must be a self‐contradicting non‐set.

Originality/value

The first time in history, it is shown that such convenient notion as the set of all real numbers needs to be reconsidered.

Keywords

Citation

Zhu, W., Lin, Y., Du, G. and Gong, N. (2008), "Inconsistency of uncountable infinite sets under ZFC framework", Kybernetes, Vol. 37 No. 3/4, pp. 453-457. https://doi.org/10.1108/03684920810863417

Publisher

:

Emerald Group Publishing Limited

Copyright © 2008, Emerald Group Publishing Limited