Exercise 3.3.2. Decide which of the following sets are compact. For those that are not compact, show how Definition 3.3.1 breaks down. In other words, give an example of a sequence contained in the given set that does not possess a subsequence converging to a limit in the set. (a) N. (b) Qn [0,1]. (c) The Cantor set. (d) {1+1/22+1/32 +...+1/n²:ne N}. (e) {1, 1/2,2/3,3/4, 4/5,...}.

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