Concept explainers
Missing irrational. Could you modify the diagonalization procedure so that the missing real you produce is a rational number? How could you modify the diagonalization argument so that the missing real number you produce is an irrational number? (Hint: Using the construction in this section, each digit of M is a 2 or a 4. Modify the construction so the 10th place, the 1000th place, and so on, are either a 3 or a 5, whereas the rest are 2 and 4’s. Why will such a number be irrational?)
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The Heart of Mathematics: An Invitation to Effective Thinking
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