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ArticleOriginal scientific text

Title

The Riemann theorem and divergent permutations

Authors 1

Affiliations

  1. Institute of Mathematics, Silesian Technical University, Kaszubska 23, 44-100 Gliwice, Poland

Abstract

In this paper the fundamental algebraic propeties of convergent and divergent permutations of ℕ are presented. A permutation p of ℕ is said to be divergent if at least one conditionally convergent series ∑an of real terms is rearranged by p to a divergent series ∑ap(n). All other permutations of ℕ are called convergent. Some generalizations of the Riemann theorem about the set of limit points of the partial sums of rearrangements of a given conditionally convergent series are also studied.

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Colloquium Mathematicum
1996/69/2
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Pages:
275-287
Main language of publication
English
Received
1994-10-10
Published
1996
Exact and natural sciences