Definition Let Xn Be A Sequence Of Real Numbers And Put Sn Sup 2n 2n 1 2 2 And Sn Inf Xn Un 1 2n 2 1 (22.54 KiB) Viewed 236 times
real analysis
please let me how to prove
· Definition! Let {xn} be a sequence of real numbers and put Sn = sup{2N, 2N+1, 2+2,...} and Sn = inf{xN, UN+1, 2N+2,... }, where N = 1, 2, .... Define lim.In = inf 3n = lim in and lim.In = sup Sn = lim sn. N>1 N+00 N>1 N+00 Prove that limen + lim yn <lim(In + yn) < lim xn + lim yn provided the left and right sides are not of the form " - 20".
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