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http://imageshack.us/a/img12/8381/37753570.jpg [Broken]

I am having trouble with this question, like I do with most analysis questions haha.

It seems like I must show that the maximum exists.

So E is compact -> E is closed

To me having E closed seems like it is clear that a maximum distance exists in the metric space but I know that more work is required.

I think the way I am supposed to solve it is by using a similar proof to the Bolzano-Weierstrass theorem, as in picking a subsequence of a subsequence but I am really not sure how to begin and really apply this to the proof.

I was thinking maybe you show that the distance between a sequence and its sub-sub sequence is in E but I am really not confident that this is correct.

Could anyone help point me in the right direction and hopefully help me gain some intuition about this stuff.

Thank you in advanced, Linda

I am having trouble with this question, like I do with most analysis questions haha.

It seems like I must show that the maximum exists.

So E is compact -> E is closed

To me having E closed seems like it is clear that a maximum distance exists in the metric space but I know that more work is required.

I think the way I am supposed to solve it is by using a similar proof to the Bolzano-Weierstrass theorem, as in picking a subsequence of a subsequence but I am really not sure how to begin and really apply this to the proof.

I was thinking maybe you show that the distance between a sequence and its sub-sub sequence is in E but I am really not confident that this is correct.

Could anyone help point me in the right direction and hopefully help me gain some intuition about this stuff.

Thank you in advanced, Linda

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