I take that back, there is still need for help.
Let be a bounded sequence for each let sup{ > } and { }. Show that there exists a sub sequence of that converges to S.
Ok so clearly > >....> .
Since it is decreasing and bounded then converges to . Futhermore there exists a subsequence of that is convergent that much also converge to S. My only problem is I don't know how to relate this back to