I'm having trouble with this problem. Could someone give me a hand?

Let S be a nonempty subset of R that is bounded above. Show that if sup S is not in S, then for every , the interval contains infinitely many elements of S.

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- September 7th 2010, 11:47 PMjackieBounded subset of R
I'm having trouble with this problem. Could someone give me a hand?

Let S be a nonempty subset of R that is bounded above. Show that if sup S is not in S, then for every , the interval contains infinitely many elements of S. - September 8th 2010, 01:09 AMCaptainBlack
- September 8th 2010, 07:14 AMjackie
Thanks a lot for your help, CB. I actually tried to assume the contrary as you suggested, but I got stuck. I have is in . So, I think I should be able to show that this lead to sup S is in S, but I don't know how.

- September 8th 2010, 11:05 AMCaptainBlack