Could someone please check my work against the definition I've provided

Please state all definitions and theorems that you will need: Definition 3.4.3 Let S be a subset of R . A point a in R is an interior point of S if there exists a neighborhood N of a such that N C S. If for every neighborhood N of x , N n S # 0 and Nn (R\\S) # 0, then x is called a boundary point of S . The set of all interior points of S' is denoted by intS' , and the set of all boundary points of S is denoted by bdS . Find the interior of each set. (Note that 0) is the empty set.) 1. The interior of 3 -: n EN is: 10 0 10 13 16 (1, 00) N O OOO O Explain: Let S = -:n EN) CR, which consists only of rational numbers. By definition 3.4.3 10 for an interior point of S, a point, x = - E R is an interior point of S if some n N(x; E) C S. Since every N(a; 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 0