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p-Adic Representation of Subsets of a Bounded Number Set

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Abstract

In this paper, we show that a ring of p-adic integers Zp can be used to represent subsets of a bounded number set. We propose an approach to define a set of p-adic balls. The union of their images is a subset of the bounded number set. The cover of the set of p-adic balls and the p-adic density of the subset of the bounded number set are defined. We also define the operations of p-adic intersection, union, and complement over sets of p-adic balls that can generate the corresponding algebra.

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Authors and Affiliations

  1. INEKS-FT Consulting Group, ul. Desyatinnaya 13а, 03011, Kiev, Ukraine

    V. P. Bocharnikov & S. V. Sveshnikov

Authors
  1. V. P. Bocharnikov
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  2. S. V. Sveshnikov
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Correspondence to V. P. Bocharnikov or S. V. Sveshnikov.

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Translated by Yu. Kornienko

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Bocharnikov, V.P., Sveshnikov, S.V. p-Adic Representation of Subsets of a Bounded Number Set. Program Comput Soft 47, 225–234 (2021). https://doi.org/10.1134/S0361768821040022

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  • DOI: https://doi.org/10.1134/S0361768821040022

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