Let S be a nonempty set that is bbd abv. Let u be the supremum of S. Show that there is a sequence in S with approaching u.
I have two general ideas on how to solve this problem, but I don't know how to start.
1) I use the epsilon definition of convergence, defining epsilon with relation to u.
2) Show that the limit cannot be less than supS (easy to prove, or not? if lim < sup S, lim is in S, choose an increasing sequence and > lim), or greater than supS.
If not(greater or less than), must be equal to.
Thanks in advance.