Geodesic
The Riemann theorem and divergent permutations
Colloquium Mathematicum, Tome 69 (1996) no. 2, pp. 275-287.

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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.
DOI : 10.4064/cm-69-2-275-287

Roman Wituła 1

1 
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Roman Wituła. The Riemann theorem and divergent permutations. Colloquium Mathematicum, Tome 69 (1996) no. 2, pp. 275-287. doi : 10.4064/cm-69-2-275-287. http://geodesic.mathdoc.fr/articles/10.4064/cm-69-2-275-287/

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