(a) Proof rigorously that if {n} is a decreasing sequence, and if it has a convergent subsequence, then {n} converges. (b) Show that there exists a sequence {n} in R such that for any y € R, there is a subsequence {n} converging to y.

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(a) Proof rigorously that if {n} is a decreasing sequence, and if it has a convergent subsequence, then {n} converges. (b) Show that there exists a sequence {n} in R such that for any y € R, there is a subsequence {n} converging to y.

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