Just a couple of hours ago, I came across a fresh publication by someone named Jonas Petrov (I believe he is an amateur mathematician of German origin) in one of the libraries. This is a non-peer-reviewed article: Petrov, J. M. (2025). On the Boundaries of Constructive Definability in Arithmetic: The Fundamental Limit of the Natural Number Sequence. Self-published. In it, he presents a rather original idea for the "limit" of natural numbers (as paradoxical as that sounds) — specifically, a natural (?) number that consists of such a vast number of digits that it leads to an "aggregation collapse" (meaning that the set of these digits no longer defines the properties of the whole number). This is a novel approach that I haven’t encountered before.
However, there is an important point to consider (even though the article presents formal proof): I don't believe that this number P can truly be considered a natural number.
Could a number like this really exist within the natural number system, or is this an example of where traditional number theory breaks down?
However, there is an important point to consider (even though the article presents formal proof): I don't believe that this number P can truly be considered a natural number.
Could a number like this really exist within the natural number system, or is this an example of where traditional number theory breaks down?
