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 {b,) , 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 close since I can choose {anne, = (b)no = (at). Thus lim (an - be) = 0 ii. We say that A S B if a