Question: (a) Prove that any non-empty finite set in (R, | |) does not have limit point, and that it is closed. (b) Given a sequence

(a) Prove that any non-empty finite set in (R, | |) does not have limit point, and that it is closed.

(b) Given a sequence (an) in (R, | |). Is the set of subsequential limits of (an) the same as the set of limit points of the set {an : n N}? Prove your assertion.

'| |' denotes the usual metric in R.

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