Question: 4. (20 points) (a) Proof rigorously that if {xn} is a decreasing sequence, and if it has a convergent subsequence, then {xn} converges. (b) Show

4. (20 points) (a) Proof rigorously that if {xn} is a

4. (20 points) (a) Proof rigorously that if {xn} is a decreasing sequence, and if it has a convergent subsequence, then {xn} converges. (b) Show that there exists a sequence {xn} in R such that for any yR, there is a subsequence {xnk} converging to y. (You can use the fact that Q is countable.)

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