Let (an)n≥1 be a bounded sequence in ℝ. Which of the following statements is FALSE?
1
If \(\rm \lim_{n\rightarrow \infty}infa_n=\lim_{n\rightarrow \infty}sup a_n, \) then (an) is convergent
2
If inf{an |n ≥ 1} = \(\rm \lim_{n\rightarrow \infty}\)sup an, then (an) is convergent
3
If sup{an|n ≥ 1} = \(\rm \lim_{n\rightarrow \infty}\) inf an, then (an) is constant
4
If sup{an|n ≥ 1} = inf {an|n ≥ 1}, then (an) is constant