Could someone please check my work

Find the interior of each set. (Note that 0) is the empty set.) 1. The interior of - :n EN , is: 0 10 13 16 (1, 00) N O Explain: Let S = -: n E N C R, which consists only of rational numbers. By definition 3.4.3 for an interior point of S, a point, x = - E R is an interior point of S if some N(x; E) C S. Since every N(ac; E) contains at least one irrational number, then there is no N(a; E) that can be contained in the set S of strictly rational numbers. Therefore, S does not have any interior points. It follows that the interior of S' is