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The Riemann theorem and divergent permutations

Roman Wituła (1996)

Colloquium Mathematicae

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.

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