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arXiv · 2304.01360

Lower and upper estimates of the quantity of algebraic numbers

Yaroslav D. Sergeyev
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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 \G1-based infinite numbers is applied to measure the set $A$ (where the number \G1 is called \emph{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 \G1-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 \G1-based numbers.

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Yaroslav D. Sergeyev. 2022-12-06. Lower and upper estimates of the quantity of algebraic numbers. https://doi.org/10.1007/s00009-022-02223-y

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