Number Theory

    

The Terminator of a Sequence: A Constructive Approach to Infinity

Authors: Gabriele Bonamini

In this paper, we introduce and develop the concept of "the terminator of a sequence", defined as the term that would be reached by extending the construction of a given infinite succession indefinitely. Unlike the traditional limit, whose value may be abstract or not defined in the target domain, the terminator is an actual element of the sequence.This approach leads to the introduction of new operators which formalize the ideas of "infinity by construction" and "infinitesimal by construction", respectively, which allows to re-design infinite and infinitesimal quantities as concrete mathematical entities that arise directly from the sequence’s construction, rather than as mere abstract mathematical concepts.

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[v1] 2025-04-04 22:07:40

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