Number Theory


Once More on Potential vs. Actual Infinity

Authors: Felix M. Lev

The {\it technique} of classical mathematics involves only potential infinity, i.e. infinity is understood only as a limit. However, {\it the basis} of classical mathematics does involve actual infinity: the infinite ring of integers $Z$ is the starting point for constructing infinite sets with different cardinalities, and it is not even posed a problem whether $Z$ can be treated as a limit of finite sets. On the other hand, finite mathematics starts from the ring $R_p=(0,1,...p-1)$ (where all operations are modulo $p$) and the theory contains only finite sets. We prove that $Z$ can be treated as a limit of $R_p$ when $p\to\infty$ and explain that, as a consequence, finite mathematics is more fundamental than classical one.

Comments: 9 Pages.

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Submission history

[v1] 2019-10-16 00:11:18

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