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References (7)
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Wujia Zhu, Yi Lin, N. Gong, Guoping Du (2008)
Wide-range co-existence of potential and actual infinities in modern mathematicsKybernetes, 37
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Wujia Zhu, Yi Lin, Guoping Du, N. Gong (2008)
The inconsistency of countable infinite setsKybernetes, 37
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Yi Lin, Wujia Zhu, N. Gong, Guoping Du (2008)
Systemic yoyo structure in human thoughts and the fourth crisis in mathematicsKybernetes, 37
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Wujia Zhu, Yi Lin, N. Gong, Guoping Du (2008)
Modern system of mathematics and a pair of hidden contradictions in its foundationKybernetes, 37
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Wujia Zhu, Yi Lin, Guoping Du, N. Gong (2008)
Modern system of mathematics and special Cauchy theater in its theoretical foundationKybernetes, 37
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Wujia Zhu, Yi Lin, N. Gong, Guoping Du (2008)
Descriptive definitions of potential and actual infinitiesKybernetes, 37
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Wujia Zhu, Yi Lin, Guoping Du, N. Gong (2008)
Inconsistency of uncountable infinite sets under ZFC frameworkKybernetes, 37
- Publisher
- Emerald Publishing
- Copyright
- Copyright © 2008 Emerald Group Publishing Limited. All rights reserved.
- ISSN
- 0368-492X
- DOI
- 10.1108/03684920810863435
- Publisher site
- See Article on Publisher Site
Abstract
Purpose – The paper aims to show using a different method that any uncountable set is a self‐contradictory non‐set. Design/methodology/approach – The paper discusses the concept. Findings – Elsewhere it is shown that in the framework of ZFC, various countable infinite sets are all self‐contradicting non‐sets. In this paper, the authors will generalize the concept of Cauchy theater, and establish the concept of transfinite Cauchy theaters. After that, employing a new method, they will prove that various uncountable infinite sets, as studied in naive set theory and modern axiomatic set theory, are also self‐contradicting non‐sets. Originality/value – The concept of general Cauchy theater is introduced.
Journal
Kybernetes – Emerald Publishing
Published: Apr 11, 2008
Keywords: Cybernetics; Set theory