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Lower and upper estimates of the quantity of algebraic numbers

Sergeyev, Yaroslav (2023) Lower and upper estimates of the quantity of algebraic numbers. Mediterranean Journal of Mathematics, 20 (12). pp. 1-10.

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Abstract

It is well known that the set of algebraic numbers (let us call it A) is countable. In this paper, instead of the usage of the classical terminology of cardinals proposed by Cantor, a recently introduced methodology using ① -based infinite numbers is applied to measure the set A (where the number ① is called grossone). Our interest to this methodology is explained by the fact that in certain cases where cardinals allow one to say only whether a set is countable or it has the cardinality of the continuum, the ① -based methodology can provide a more accurate measurement of infinite sets. In this article, lower and upper estimates of the number of elements of A are obtained. Both estimates are expressed in ① -based numbers.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Sergeyev, Yaroslavyaro@dimes.unical.it0000-0002-1429-069X
Keywords: Algebraic numbers, infinite sets, counting systems, grossone.
Subjects: Specific Sciences > Cognitive Science > Computation
Specific Sciences > Cognitive Science > Concepts and Representations
Specific Sciences > Mathematics
Specific Sciences > Cognitive Science > Perception
Depositing User: Prof. Yaroslav Sergeyev
Date Deposited: 04 Oct 2024 16:02
Last Modified: 04 Oct 2024 16:02
Item ID: 23986
Journal or Publication Title: Mediterranean Journal of Mathematics
Publisher: Springer
Official URL: https://link.springer.com/article/10.1007/s00009-0...
DOI or Unique Handle: 10.1007/s00009-022-02223-y
Subjects: Specific Sciences > Cognitive Science > Computation
Specific Sciences > Cognitive Science > Concepts and Representations
Specific Sciences > Mathematics
Specific Sciences > Cognitive Science > Perception
Date: 2023
Page Range: pp. 1-10
Volume: 20
Number: 12
URI: https://philsci-archive.pitt.edu/id/eprint/23986

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