really.smarty
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- Joined
- Oct 10, 2009
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{xn} is in [an,bn] which is a nested squence of closed intervals. prove xn is convergent?
Let {[an,bn]} be a nested sequence of closed intervals. Also assume that {bn-an} --> 0. Let {xn} be a sequence such that xn is in [an,bn] for all n. Prove that [xn] converges. (Hint, prove that {xn} is cauchy).
i am having trouble with this because any information i get regarding nested sequences talks about particular points in the sequence, yet this is another sequence xn being in the nested sequence, so i am not sure how to go about proving that.
thank you.
Let {[an,bn]} be a nested sequence of closed intervals. Also assume that {bn-an} --> 0. Let {xn} be a sequence such that xn is in [an,bn] for all n. Prove that [xn] converges. (Hint, prove that {xn} is cauchy).
i am having trouble with this because any information i get regarding nested sequences talks about particular points in the sequence, yet this is another sequence xn being in the nested sequence, so i am not sure how to go about proving that.
thank you.