I begin with a quote, because I could not formulate better my starter thoughts of this writing. The quote is from the early 60s, but today it is still up-to-date.

"... The whole of modern mathematics is essentially based on the concept (or idea) of the intense actual infinity. In set theory there is much less developed extensive idea of infinity. Cantor's predecessor, Bolzano, whose views have greatly influenced the formation of set theory, trying to find a solution to the infinite quantity (extensive infinity) problem. However, the set theory was formed as a very rich theory of intensive infinity, while the extensive concept of infinity was essentially a stranger."¹

Cantor's concept of infinity is about extensive infinity, but he did not link this concept with intensive infinity. There is no connection between extensive and intensive infinity although there is an operation: the reciprocal function, which could lead from one to the other. The reason for the lack of resolution is "the gap between the continuum and discreteness" as it is called by A.A. Fraenkel and J. Bar-Hillel².

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¹G.I.Naan, Infinity and the Universe, „Idea of infinity in mathematics and cosmology" (The quote is not the original text, it is translated from Hungarian.)

²A.A. Fraenkel , J. Bar-Hillel, Foundations of Set Theory

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