It may be remarked that the computable numbers, on the other hand, are countable. To count them we just list, in numerical order, those Turing machines which generate real numbers (i.e. which produce the successive digits of real numbers). We may wish to strike from the list any Turing machine which generates a real number that has already appeared earlier in the list. Since the Turing machines are countable, it must certainly be the case that the computable real numbers are countable. Why can we not use the diagonal slash on that list and produce a new computable number which is not in the
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