Could someone please check my work

2. The set of natural numbers, N, is: Open Closed Neither Explain: WTS N is closed: n E N and n E N(n; E) for any n E N Since N(n; E) n N # 0 and N(n; E) n (R\\N) # 0, then by definition 3.4.3 for the boundary of N , N is in the boundary of N . Therefore, the boundary of N is N by definition 3.4.3. Since bd N = N , then by definition 3.4.6, since N contains all of its boundary, then N is closed. WTS N is not open: Let N C R , which consists only of natural numbers. By definition 3.4.3 for an interior point of N, a point, n E R is an interior point of N if some N(n; &) C N. Since every N n; contains at least one number that is not a natural number, then there is no N/H N/P N n; that can be contained in the set N of strictly natural numbers. Therefore, N does not have any interior points. It follows that the interior of N is 0. Since N does not have any interior points, then by definition 3.4.7(a), N is not open