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## The Riemann theorem and divergent permutations

### Tom 69 / 1996

Colloquium Mathematicum 69 (1996), 275-287 DOI: 10.4064/cm-69-2-275-287

#### Streszczenie

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 $∑ a_n$ of real terms is rearranged by p to a divergent series $∑ a_{p(n)}$. 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.

• Roman Wituła

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