I have this question:
i) Show: If (an) is a bounded sequence and ℓ := lim inf (an), then for any ǫ > 0
there exists N(ǫ) such that an > ℓ − ǫ for all n ∈ N with n ≥ N(ǫ).
Show first that am ≥ cn for all m ≥ n. Then show that cn > ℓ − ǫ for n
sufficiently large.
I just not sure what to do. I am useless at these things.