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Cantor supposes we may make an infinite list of real numbers between 0 and 1 and pair them with Natural Numbers. Then he supposes we make another real number by changing digits along a diagonal in the list. We take the first digit of the first number and change it, take the second digit from the second number and add one to it, and so on. Then he says that we constructed a number not on the list.

My objection is that in order to conclude this we must be able to state that the digit at…

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