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References (12)
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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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(2008)
2008h), “New Berkeley’s paradox in the theory of limits -
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)
Cauchy theater phenomenon in diagonal method and test principle of finite positional differencesKybernetes, 37
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Wujia Zhu, Yi Lin, Guoping Du, N. Gong (2008)
The inconsistency of the natural number systemKybernetes, 37
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Wujia Zhu, Yi Lin, N. Gong, Guoping Du (2008)
New Berkeley paradox in the theory of limitsKybernetes, 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)
Modern system of mathematics and general Cauchy theater in its theoretical foundationKybernetes, 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
- 10.1108/03684920810863471
- Publisher site
- See Article on Publisher Site
Abstract
Purpose – Aims to focus on the co‐existence of potential and actual infinities in modern mathematics and its theoretical foundation. It has been shown that not only the whole system of modern mathematics but also the subsystems directly dealing with infinities have permitted the co‐existence of these two kinds of infinities. Design/methodology/approach – The paper discusses the issues surrounding the two problems that urgently need to be solved. One of the problems is how to select an appropriate theoretical foundation for modern mathematics and the theory of computer science. The other problem is, under what interpretation can modern mathematics and the theory of computer science be kept in their entirety? Findings – This paper constructs the mathematical system of potential infinities in an effort to address the two afore‐mentioned problems. Originality/value – Highlights that the said mathematical system of potential infinities is completely different of the mathematical system constructed on the basis of intuitionism.
Journal
Kybernetes – Emerald Publishing
Published: Apr 11, 2008
Keywords: Cybernetics; Set theory