For 0 <α< 1, let I(α) = {x : 1 − α

of numbers satisfying 0 < αn < 1 for all n, and let An = I(αn). (i) Find lim sup An and lim inf An. (ii) Find conditions, expressed in terms of αn, under which lim An exists, and find this limit. (iii) Define J(α) = {x : 1 − α ≤ x ≤ 1 + α} and Bn = J(αn). Answer questions (i) and (ii) for sequence {Bn}.