Exercise 1: (An instance of Cantor) Let {X1, X2, 23, ...} be an infinite list of particular real numbers in the interval [0, 1). For each i E {1, 2, 3, ...} the unique decimal expansion of X; is: xi = > ajj10 3 = 0.ai,1di,20i,3 . . . j=1 Assume that the first few numbers on the list are: 21 = 0.9701022293 . .. x2 = 0.0003332240 . .. 3 = 0.2222994000 . . . 4 = 0.1230032882 . .. 25 = 0.7487245781 . .. Define b = _ 1 b; 10- where bj = if ajj = 2 2 if ajj # 2 Vje { 1, 2, 3, . . .} a) Write the first 5 digits of the decimal expansion of b. Is be [0, 1)? b) Does the given decimal expansion of b have an infinite tail of 9s? c) Is b = x1? Is b = x5? Is b = x7? Is be {x1, X2, 23, ...}