Chapter 3.3, Problem 15MS

The first digit (H). Suppose that, in constructing the number M in the Cantor diagonalization argument, we declare that the first digit to the right of the decimal point of M will be 7, and then the other digits are selected as before (if the second digit of the second real number has a 2, we make the second digit of M a 4; otherwise, we make the second digit a 2, and so on). Show by example that the number M may, in fact, be a real number on our list.