Let (an)n≥1 be a bounded sequence of real numbers such that \(\rm \lim_{n\rightarrow \infty}a_n\) does not exist. Let S = {l ∈ ℝ : there exists a subsequence of (an) converges to l}.
Which of the following statements are necessarily true?
1
S is the empty set
2
S has exactly one element
3
S has at least two elements
4
S has to be a finite set