In this paper a problem of approximatingthe real numbers by using the series of real numbers is considered.It is proven that if the given family of sequences of real numbers satisfiessome conditions of set-theoretical nature, like being closed under initial subsequencesand (additionally) possessing properties of adding and removing elements, then it automatically possessessome approximating properties, like, for example, reaching supremum of the set of sums of subseries.
@article{222,
title = {On certain approximation problem connected with the sums of subseries},
journal = {Tatra Mountains Mathematical Publications},
volume = {55},
year = {2013},
doi = {10.2478/tatra.v55i0.222},
language = {EN},
url = {http://dml.mathdoc.fr/item/222}
}
Wituła, Roman; Kaczmarek, Konrad; Hetmaniok, Edyta; Słota, Damian. On certain approximation problem connected with the sums of subseries. Tatra Mountains Mathematical Publications, Tome 55 (2013) . doi : 10.2478/tatra.v55i0.222. http://gdmltest.u-ga.fr/item/222/