... generated by any one of the following:1. the collection of all intervals of the form (x, ∞),2. the collection of all intervals of the form (x, y],3. the collection of all intervals of the form [x, ... the set of all sequences whose terms are the digits 0 and 1.Then, E is uncountable.PROOF. Let A be a countable subset of E. Let x1, x2, . . . be an enumeration of theelements of A, that ... (x+n) denote the subsequence consisting of the positive elements of (xn) and let (x−n) denote the subsequence of negative elements of (xn). Both of these sequences must be infinite.2. Both...