2. Suppose that A and B are two (non-empty) subsets of R. In this problem, N = {0, 1, 2, 3 ... }. We define the following new concepts: i. We say that A is close to B if there exist sequences {an}, and {on}me, such that an E A and bn E B for all n E N, and lim (an - bn) = 0. For example, we can say A = R and B = Q are n-00 100 close since I can choose {an}no = {bn}= 120 = In2+1) n=0 Thus lim (an - bn) = 0 ii. We say that A 9 - 0 7's a = q'V = DE'O