Ok, so i did this proof and I'm unsure about it?
I wnat to prove that
has a convergent subsequence.
Proof:
Since
is a bounded sequence of real numbers, it must have at least one accumulation point. Let A be that accum pt. By definition, A is an accum pt of
iff each neighborhood contains points of
which are not A. Let
be arbitrary. So, we can let
elemnet of (A-
,A+
). As
,(A-
,A+
) accumulates at A. Therefore, A is an accum pt of
.
I'm afraid I wasn't specific enough and should have included the case for finitely many distinct terms.