Abstract
PurposeThis paper is the fourth part of the effort to resolve the following two problems that urgently need an answer: how can an appropriate theoretical foundation be chosen for modern mathematics and computer science? And, under what interpretations can modern mathematics and the theory of computer science be kept as completely as possible?Design/methodology/approachThe paper is a conceptual discussion.FindingsThe paper lays out the set theoretical foundation for the mathematical system of potential infinities.Originality/valueThis work is the non‐logical axiomatic part of the mathematical system of potential infinities: the axiomatic set theoretic system. At the end, the problem of consistency of this axiomatic set theory is discussed.
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