ABSTRACT

R. Then we can apply the same process to S2. Namely, by the Riemann theorem, there is a permutation Q2 of the series S2 such that Q2S2 = i=1 Ci converges to the number a2. By the definition of the convergence of series, there is some number k2 such that | i=1mci - u2| < ¼ for any m > k2. The proof of the Riemann theorem [41] or the properties of convergent series show that it is possible to take such permutation Q1 that changes places only for a finite number of elements from S2. So, there is the least number h2 such that Q2 does not move elements from S2 with larger indices.