Suppose is a real valued function whose domain contains the interval . Assume that is unbounded on .
(a) Prove that there exists a sequence in that converges to such that for every , .
Isn't this just the definition of an unbounded sequence? Do we have to actually construct one? What would be the easiest way to do this?
(b) Using this unbounded sequence how would we show that the set of Riemann sums of corresponding ot is an unbounded set of real numbers?