(a) Show that there are at least as many irrational numbers (nonrepeating decimals) as there are terminating decimals. [Hint: With each terminating decimal associate a nonrepeating decimal.]
(b) Show that there are at least as many irrational numbers as there are repeating decimals. [Hint: With each repeating decimal, associate a nonrepeating decimal by inserting longer and longer strings of zeros: for instance, with .11111111 ⋯ associate the number .101001000100001 ⋯.]
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