Problem of infinity between predicates and infinite sets

Problem of infinity between predicates and infinite sets Purpose – The paper's aim is to reconsider the feasibility at both the heights of mathematics and philosophy of the statement that each predicate determines a unique set. Design/methodology/approach – A conceptual approach is taken. Findings – In the naive and the modern axiomatic set theories, it is a well‐known fact that each predicate determines precisely one set. That is to say, for any precisely defined predicate P , there is always A ={ x | P ( x )} or x ∈ A ↔ P ( x ). However, when the authors are influenced by the thinking logic of allowing both kinds of infinities and compare these two kinds of infinities, and potentially infinite and actually infinite intervals and number sets, it is found that the expressions of these number sets are not completely reasonable. Originality/value – Detailed analyses are given for the introduction of new symbols and representations for either potential or actual infinite sets. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Kybernetes Emerald Publishing

Problem of infinity between predicates and infinite sets

Kybernetes, Volume 37 (3/4): 8 – Apr 11, 2008
8 pages

/lp/emerald-publishing/problem-of-infinity-between-predicates-and-infinite-sets-Ow4UcLUdTE
Publisher
Emerald Publishing
ISSN
0368-492X
DOI
10.1108/03684920810863516
Publisher site
See Article on Publisher Site

Abstract

Purpose – The paper's aim is to reconsider the feasibility at both the heights of mathematics and philosophy of the statement that each predicate determines a unique set. Design/methodology/approach – A conceptual approach is taken. Findings – In the naive and the modern axiomatic set theories, it is a well‐known fact that each predicate determines precisely one set. That is to say, for any precisely defined predicate P , there is always A ={ x | P ( x )} or x ∈ A ↔ P ( x ). However, when the authors are influenced by the thinking logic of allowing both kinds of infinities and compare these two kinds of infinities, and potentially infinite and actually infinite intervals and number sets, it is found that the expressions of these number sets are not completely reasonable. Originality/value – Detailed analyses are given for the introduction of new symbols and representations for either potential or actual infinite sets.

Journal

KybernetesEmerald Publishing

Published: Apr 11, 2008

Keywords: Cybernetics; Number theory; Set theory

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