Hi,

I had a problem proving this theorem:

Let {sn} be a bounded sequence of real numbers. Assume S = {sn: n= 1, 2, ...} is infinite. Then {sn} is convergent if and only if S has exactly one accumulation point.

But in another page of my notebook, it says:

Accumulation points can be more than one or even infinitely many while the limit is unique.

Are they opposite? Thanks for any help.