A sequence diverges if it has a subsequence which diverges.
Is this statement true? Is there a counterexample?
(Intuitively I would say this is false.)
I suppose I'm stuck because I'm reading this question as follows: If a sequence has a subsequence which diverges, then the sequence diverges.
I just keep thinking there is a counterexample to this.
Is it a fact that if there is a divergent subsequence the whole sequence diverges?