Chapter 3.3, Problem 16MS

Ones and twos (H). Show that the set of all real numbers between 0 and 1 just having l’s and 2’s after the decimal point in their decimal expansions has a greater cardinality than the set of natural numbers. $\text{(So, the number 0}\text{.112111122212122211112}\mathrm{...}$ is anumber in this set, $\text{but 0}\text{.1 161221212122122}\mathrm{...}$ is not, because it contains digits other than just l’s and 2’s.)