8. (10pt) Show that the power set of the set of positive integers (i.e., P(Z+)) is uncountable. (Hint: Assume that there is a one-to-one correspondence from Z+ to P(Z+). Represent a subset of Z+ as an infinite bit string with ith bit 1 if i belongs to the subset and 0 otherwise. Suppose that you can list those infinite strings in a sequcne indexed by the positive integers. Construct a new bit string with its ith bit equal to the complement of the ith bit of the ith string in the list. Show that this new bit string cannot appear in the list