Prove that a bounded sequence

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a) Let {xn} be a bounded sequence. Prove that if limn→∞ sup |xn| = 0, then limn→∞ xexists and equals 0.

(b)  Prove that a bounded sequence that does not converge always has at least two subsequences that converge to different limits.

(c)  Find the limit inferior and limit superior of the sequence {an} if an = ⌊sin n⌋ for all n ∈ N.

(d)  Find the set of all subsequential limits for the sequence {xn} if for all n ∈ N

Reference no: EM131396656

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