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References (5)
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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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W.J. Zhu, X.A. Xiao, F.M. Song, H.F. Gu
An outlook on infinity (III): ‘every’ and ‘all’ -
Yi Lin, Wujia Zhu, N. Gong, Guoping Du (2008)
Systemic yoyo structure in human thoughts and the fourth crisis in mathematicsKybernetes, 37
-
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, N. Gong, Guoping Du (2008)
Descriptive definitions of potential and actual infinitiesKybernetes, 37
- Publisher
- Emerald Publishing
- Copyright
- Copyright © 2008 Emerald Group Publishing Limited. All rights reserved.
- ISSN
- 0368-492X
- DOI
- 10.1108/03684920810863408
- Publisher site
- See Article on Publisher Site
Abstract
Purpose – The paper aims to show countable infinite sets are self‐contradictory non‐sets. Design/methodology/approach – The paper is a conceptual discussion. Findings – Since, long ago, it has been commonly believed that the establishment and development of modern axiomatic set theory have provided a method to explain Russell's paradox. On the other hand, even though it has not been proven theoretically that there will not appear new paradoxes in modern axiomatic set theory, it has been indeed a century that no one has found a new paradox in modern axiomatic set theory. However, when we revisit some well‐known results and problems under the thinking logic of allowing two kinds of infinities, we discover that various countable infinite sets, widely studied and employed in modern axiomatic set theory, are all specious non‐sets. Originality/value – A well‐known concept is shown to be not as correct as what has been believed.
Journal
Kybernetes – Emerald Publishing
Published: Apr 11, 2008
Keywords: Cybernetics; Set theory