4. (12 marks total) Let I = [0,1] and consider the following construction: remove the open interval (1 /3, 2/3) (the open middle third portion of I) from I. This leaves us with the union of the two intervals [0, 1 / 3] and [2/3, 1]. Then, we remove the open mid dle third from each of these intervals, resulting in the four intervals [0, 1/9], [2/9, 1 / 3], [2/3, 7/9], and [8/9, 1]. We repeat this process indenitely, removing the open middle third from every interval that remains from the preceding step. The set of all numbers in [0,1] that remain after all these open middle third intervals have been removed is called the Cantor ternary set, or simply Cantor set, named after the German maths ematician George Cantor (18451918). A graphical representation of the construction of the Cantor set is shown below. (a) (5 marks) Given an interval ((1,1)) C R with a.