1. Let Z be the set of real numbers in the open interval (0, 1) with only 1s and 2s in the

decimal expansion. (NOTE: 0.1 & 2 because it has infinitely many Os in its decimal

expansion!) Prove that there is no bijection between N and Z, using an adapted version of

the diagaonlization argument we used in class to prove that there is no bijection between N

and (0,1). A good start would be to make sure Z replaces every (0, 1) in the argument, but

that's not enough - read carefully and make sure that your sentences apply to Z!