Let be a bounded function such that for any partition P of [a,b].

Prove that there exists a constant c such that for any x in [a,b] (by contradiction) .

Appreciate if someone could help on this one. Thanks...

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- December 13th 2008, 03:11 PMseniorcalculusLower and Upper Darboux Sums
Let be a bounded function such that for any partition P of [a,b].

Prove that there exists a constant c such that for any x in [a,b] (by contradiction) .

Appreciate if someone could help on this one. Thanks... - December 13th 2008, 04:25 PMNonCommAlg
- December 13th 2008, 04:46 PMseniorcalculus
Okay, thanks. But that's a direct proof, right? I kinda need help for proof by contradiction though.

- December 13th 2008, 05:09 PMNonCommAlg
- December 13th 2008, 05:28 PMseniorcalculus
Okay, I understand it now. Thanks, NonCommAlg (Wink)

But, I realized that you have picked an instance of a partition in this case, which is P={a,b}. But in the proof we have to show that for any partition interval. Shouldn't we have to assume for any partition P?