Let bounded above, prove that

How to prove this? I think is not that easy.

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- Mar 25th 2011, 02:54 PMConnectedIterated sup
Let bounded above, prove that

How to prove this? I think is not that easy. - Mar 25th 2011, 03:32 PMDrexel28
Let be fixed. We clearly then that that and moreover it's clear that putting these two together gives and since was arbitrary it follows that . Conversely, fix and then evidently . Since was arbitrary we have that and since was arbitrary . The conclusion follows.

- Mar 25th 2011, 04:45 PMConnected
- Mar 25th 2011, 04:49 PMDrexel28