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References (8)
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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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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, Guoping Du, N. Gong (2008)
The inconsistency of countable infinite setsKybernetes, 37
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10.1108/03684920810863435
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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
- 10.1108/03684920810863444
- Publisher site
- See Article on Publisher Site
Abstract
Purpose – The paper's purpose is to show a class of well‐used methods in set theory is invalid. Design/methodology/approach – A conceptual approach is taken. Findings – Based on the concept of Cauchy theater introduced elsewhere, it is proven that the argument employing the diagonal method for the fact that the set of all real numbers R ={ x | r ( x )}, where r ( x )= df “ x is a real number” has an uncountable cardinality, is not valid. The diagonal method has appeared in naive and modern axiomatic set theories. Originality/value – Point out more paradoxes in the methodology of mathematics.
Journal
Kybernetes – Emerald Publishing
Published: Apr 11, 2008
Keywords: Cybernetics; Set theory