Cantor went after irrationals, a messy set for mathematicians. Prove that irrationals have the cardinality of the continuum. (There are many more irrationals than rationals.) (a) In binary, consider the number x = 0.1011011011011 · · · = 0.1011. Show that x = 5 7 . Argue that a rational number’s binary representation either terminates or some bits eventually repeat. (You don’t need a full proof.)