Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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 (doi: 10.20944/preprints202110.0389.v1). Averbukh, B. A Formalization of the Concept of a Numeral System. Preprints 2021, 2021100389 (doi: 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

MATHEMATICS & COMPUTER SCIENCE, Geometry & Topology

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