Article
Version 1
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A Formalization of the Concept of a Numeral System
Version 1
: Received: 25 October 2021 / Approved: 26 October 2021 / Online: 26 October 2021 (14:15:22 CEST)
How to cite: Averbukh, B. A Formalization of the Concept of a Numeral System. Preprints 2021, 2021100389. https://doi.org/10.20944/preprints202110.0389.v1 Averbukh, B. A Formalization of the Concept of a Numeral System. Preprints 2021, 2021100389. https://doi.org/10.20944/preprints202110.0389.v1
Abstract
We consider finite and unconditionally convergent infinite expansions of elements of a given topological monoid G in some base B c G as words of the alphabet B, identify insignificantly different words and define a multiplication and a topology on the set of classes of these words. Classical numeral systems are particular cases of this construction. Then we study algebraic and topological properties of the obtained monoid and, for some cases, find conditions under which it is canonically topologically isomorphic to the initial one.
Keywords
topological monoid; numeral system
Subject
Computer Science and Mathematics, Geometry and Topology
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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