Mark each statement True or False. Justify each answer. (a) A sequence (s n ) converges to s iff every subsequence of (s n ) converges to s. (b) Every bounded sequence is convergent. (c) Let (s n ) be...

Mark each statement True or False. Justify each answer.

(a) A sequence (s_n) converges to s iff every subsequence of (s_n) converges to s.

(b) Every bounded sequence is convergent.

(c) Let (s_n) be a bounded sequence. If (s_n) oscillates, then the set S of subsequential limits of (s_n) contains at least two points.

(d) Let (s_n) be a bounded sequence and let m = lim sup s_n. Then for every ε > 0 there exists N ∈ N such that n ≥ N implies that s_n
> m − ε .

(e) If (s_n) is unbounded above, then (s_n) contains a subsequence that has +
 as a limit.