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.
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?
This paper constructs the mathematical system of potential infinities in an effort to address the two afore‐mentioned problems.
Highlights that the said mathematical system of potential infinities is completely different of the mathematical system constructed on the basis of intuitionism.
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