I'm a little stuck on this question:
Let S be a nonempty bounded subset of and let . Show that
so far I have:
therefore is a upper bound of .
That's what I have so far.
Then is finite, therefore, we know that
To complete the proof, we have to show that holds, where .
Note that .
Multiplying both sides of (1) with , we get
which is equivalent to
This proves that , which is the desired identity.
You may wish to check the following book:
Introduction to Calculus and ... - Google Book Search