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

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 NV of a such that NV C S. If for every neighborhood N of a , N n S # 0 and Nn (R\\ S) # 0, then a 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 . 2. The boundary of [0, 11) U (11, 14) is: 0 [0, 11] {0, 11} {0, 11, 14} $6919 Explain: Let S = [0, 11) U (11, 14) . O E S and O E N(0; E). Since N(0; E) n S # 0 andN(0; E) n (R\\ S) # 0, then by definition 3.4.3 for the boundary of S , 0 is in the boundary of S . Also, 11 & S but 11 E N(11; E) . Since N(11; E) n S * 0 and N(11; E) n (R\\S) # 0, then by definition 3.4.3 for the boundary of S , 11 is a boundary point of S . smelgusoo all wit box Also, 14 & S but 14 E N(14; E) . Since N(14; E) n S # 0 and N(14; E) n (R\\ S) # 0, then by definition 3.4.3 for the boundary of S , 14 is a boundary point of S . Therefore, the boundary of S is {0, 11, 14}