Mark each statement True or False. Justify each answer.
(a) Every sequence has a convergent subsequence.
(b) The set of subsequential limits of a bounded sequence is always non-empty.
(c) (sn) converges to s iff lim inf sn = lim sup sn = s.
(d) Let (sn) be a bounded sequence and let m = lim sup sn. Then for every ε > 0 there are infinitely many terms in the sequence greater than m − ε.
(e) If (sn) is unbounded above, then lim inf sn = lim sup sn = +∞.
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