]> Exercise 1.6

Exercise 1.6

Are all such sequences countable?

Solution:

No! If you had a list of all of them, you can imagine a number that differs from every one of them because it differs from the n-th in the n-th decimal place. (If the n-th entry on the list had 5 in the n-th place give your number the value 7 in that place, otherwise give it 5.)

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