Could someone please check my work

Find The boundary of The Set [0, 2] n [ 2, 4] Answer : 10, 43 Justification : 0 and 4 are boundary points of The ser because the Smallest E-neighborhood around them falls both inside and ourside The car. 2 is nor a boundary point because The smallest E-neighbor hood around it only falls inside the ser. Classify the following set as open, closed, neither, or both: S = {x:x'> 0] S = ( - 00, 0 ) U (0, 50 ) Justification! Answer: S is open The boundary of S is Eof Since The smallest S is not closed E-neighborhood around it falls inside The ser and Justification : outside The Set of zero. A ser is closed iff its complement is open . The The ser is unbounded or complement of set, S is -0 and OD, So - 00 and 203. This is an isolated . are not boundary points boundary point . IT is a Since 0. is not contained boundary point since The in The ser, S, Then The Smallest E- neighborhood Ser is open. around it falls both inside The ser or zero and outside The ser. Since O is Contained in The Ser, SC= EOS, Then S" is closed Since SC is closed, Then S is not closed