• Cows Look Like Maps
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    7 months ago

    In fact, there’s infinite problems that cannot be solved by Turing machnes!

    (There are countably many Turing-computable problems and uncountably many non-Turing-computable problems)

    • @MBM
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      -17 months ago

      Infinite seems like it’s low-balling it, then. 0% of problems can be solved by Turing machines (same way 0% of real numbers are integers)

      • Cows Look Like Maps
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        27 months ago

        Infinite seems like it’s low-balling it

        Infinite by definition cannot be “low-balling”.

        0% of problems can be solved by Turing machines (same way 0% of real numbers are integers)

        This is incorrect. Any computable problem can be solved by a Turing machine. You can look at the Church-Turing thesis if you want to learn more.

        • @MBM
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          17 months ago

          Infinite by definition cannot be “low-balling”.

          I was being cheeky! It could’ve been that the set of non-Turing-computible problems had measure zero but still infinite cardinality. However there’s the much stronger result that the set of Turing-computible problems actually has measure zero (for which I used 0% and the integer:reals thing as shorthands because I didn’t want to talk measure theory on Lemmy). This is so weird, I never got downvoted for this stuff on Reddit.

      • @DaleGribble88@programming.dev
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        17 months ago

        The subset of integers in the set of reals is non-zero. Sure, I guess you could represent it as arbitrarily small small as a ratio, but it has zero as an asymptote, not as an equivalent value.

        • @MBM
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          17 months ago

          The cardinality is obviously non-zero but it has measure zero. Probability is about measures.