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4. (12 marks total) Let / = 10, 1] and consider the following construction: remove the open interval (1/3, 2/3) (the open middle third portion of /) 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 indefinitely, 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 math- ematician George Cantor (1845-1918). A graphical representation of the construction of the Cantor set is shown below, (a) (5 marks) Given an interval (a, b) C R with a