Let [], be closed intervals with [] [] for all . Prove that I know it has something to do with compactness, but I am not sure how to proceed.
Last edited by Pythagorean12; Dec 1st 2009 at 02:07 PM.
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Originally Posted by Pythagorean12 Let [], be closed intervals with [] [] for all . Prove that I know it has something to do with compactness, but I am not sure how to proceed. What have you tried?!
The requirement that implies that . So has a least upper bound. Call it . Show that .
The statement implies that The bounded colsed interval collection has finite intersection property,thus the intersection is nonempty.
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