Question: Let (sn) be a sequence and f : N N a bijective map (we do not assume that it preserves order). Let tn = sf

Let (sn) be a sequence and f : N N a bijective map (we do not assume that it preserves order). Let tn = sf (n). For each of the following questions, give a proof if your answer is yes, and a counterexample if your answer is no: (a) If (sn) converges, does (tn) converge? If yes, are the limits equal? (b) Let S and T be the sets of subsequential limits of (sn) and (tn), respectively. Is it true that S = T

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