Let S = {0, 1, 2, ... } be the set of all integers. For A ⊂ S, let fn(A) be the number of elements in the intersection A ∩ {0, 1, ...,n}. Let A be the class of all sets A for which the limit exists. Show that A is not a field. [Hint: Let A1 = {1, 3, 5, ... } and A2 ={ all odd integers between 22n and 22n+1 and all even integers between 22n+1 and 22n+2 for n = 0, 1, ... }. Show that both A1 and A2 are in A but A1 ∩ A2 ∈ A/ .]