Let so that then prove that if is bounded above, so is and

First part is easy, now since we have that Is this correct?

Now suppose is bounded below, we have

If is bounded below so does then where Is it correct?

Thanks!

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- March 29th 2011, 02:59 PMConnectedsup and inf
Let so that then prove that if is bounded above, so is and

First part is easy, now since we have that Is this correct?

Now suppose is bounded below, we have

If is bounded below so does then where Is it correct?

Thanks! - March 29th 2011, 08:06 PMbkarpuz
Correct

Correct

In such questions, I can suggest you to always mention the domains of the variables, i.e.,

Assume that for all , then

we have

for all ,

which implies that (dont forget that is constant and is independent of )

is bounded below by a constant , and thus,

for all . - March 30th 2011, 03:02 AMConnected
Yes of course, it's just to save writing, that's all!