Problem of infinity between predicates and infinite sets

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.

Citation

Zhu, W., Lin, Y., Gong, N. and Du, G. (2008), "Problem of infinity between predicates and infinite sets", Kybernetes, Vol. 37 No. 3/4, pp. 526-533. https://doi.org/10.1108/03684920810863516