Inconsistency of uncountable infinite sets under ZFC framework
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)=df “x 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