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?
In such questions, I can suggest you to always mention the domains of the variables, i.e.,
Assume that for all , then
for all ,
which implies that (dont forget that is constant and is independent of )
is bounded below by a constant , and thus,
for all .