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Using grossone to count the number of elements of infinite sets and the connection with bijections

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Abstract

In this paper, we look at how the notion of bijections can be used within the frame of Sergeyev’s numeral system. We give two definitions for counting the number of elements of a set and we explore the connections between these two definitions. We also show the difference between this new numeral system and the results of the traditional naive set theory.

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Authors and Affiliations

  1. Laboratoire d’Informatique Théorique et Appliquée, EA 3097, Université Paul Verlaine — Metz, UFR-MIM, Île du Saulcy, 57045, Metz Cedex, France

    Maurice Margenstern

  2. CNRS, LORIA, Nancy, France

    Maurice Margenstern

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  1. Maurice Margenstern
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Correspondence to Maurice Margenstern.

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The text was submitted by the author in English.

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Margenstern, M. Using grossone to count the number of elements of infinite sets and the connection with bijections. P-Adic Num Ultrametr Anal Appl 3, 196–204 (2011). https://doi.org/10.1134/S2070046611030034

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  • DOI: https://doi.org/10.1134/S2070046611030034

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