Problem 3. The Cantor set is a subset of the unit interval 0,1]. To construct the Cantor set, 1 2 start by removing the middle third 3' from the interval. Next remove the middle third of 3 what remains. Continue indefinitely. The Cantor set is all the numbers that remain. a) Write the series for the lengths removed and find the sum of the series b) Let n be in the Cantor set, how do we actually find n? c) Let On be the total length left after n steps. Determine lim On