Let (xn) be a bounded sequence, and for each n EN let sn := sup{xk : k 2: n} and tn :=
Chapter 3, Problem 10(choose chapter or problem)
Let (xn) be a bounded sequence, and for each n EN let sn := sup{xk : k 2: n} and tn := inf{xk : k 2: n}. Prove that (sn) and (tn) are monotone and convergent. Also prove that if 1im(sn) = lim(t ), then (x ) is convergent. [One calls limes ) the limit superior of (x ), and lim (t ) the n n n n n limit inferior of (xn ).]
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