Playing with Infinity – Footnote 2

 

Although I constructed the new number by using the first digit in the first number on the list, the second digit in the second number, and so on, I could equally have chosen any digit from the first number on the list, any digit from the second, and so on, as long as I was careful to pick a digit from a different decimal place each time.  Using the diagonal method just makes it easier to keep track of where you are in the process, but you can see that by picking the digits in different ways, there is not just one, but an infinite number of real numbers that are not on the list.

 

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