<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper a problem of approximating the real numbers by using the series of real numbers is considered. It is proven that if the given family of sequences of real numbers satisfies some conditions of set-theoretical nature, like being closed under initial subsequences and (additionally) possessing properties of adding and removing elements, then it automatically possesses some approximating properties, like, for example, reaching supremum of the set of sums of subseries.</p></abstract>

In this paper a problem of approximating the real numbers by using the series of real numbers is considered. It is proven that if the given family of sequences of real numbers satisfies some conditions of set-theoretical nature, like being closed under initial subsequences and (additionally) possessing properties of adding and removing elements, then it automatically possesses some approximating properties, like, for example, reaching supremum of the set of sums of subseries.

On Certain Approximation Problem Connected with the Sums of Subseries

Institute of Mathematics Silesian University of Technology Kaszubska 23 PL–44-100 Gliwice POLAND

Tatra Mountains Mathematical Publications

{"article-title":"On Certain Approximation Problem Connected with the Sums of Subseries"}

In this paper a problem of approximating the real numbers by using the series of real numbers is considered. It is proven that if the given family of sequences...

On Certain Approximation Problem Connected with the Sums of Subseries

Published Online: Aug 13, 2013

Page range: 37 - 45

DOI: https://doi.org/10.2478/tmmp-2013-0017

Keywords
approximation by sums of subseries, property of sets closed under initial subsequences, properties of adding and removing elements

This content is open access.

On Certain Approximation Problem Connected with the Sums of Subseries

Published Online: Aug 13, 2013

Page range: 37 - 45

DOI: https://doi.org/10.2478/tmmp-2013-0017

Keywordsapproximation by sums of subseries, property of sets closed under initial subsequences, properties of adding and removing elements

This content is open access.

Keywords
approximation by sums of subseries, property of sets closed under initial subsequences, properties of adding and removing elements