Comment on this one goes out to the arts & humanities

• MBM@lemmings.world ⁨8⁩ ⁨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)

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  • CowsLookLikeMaps@sh.itjust.works ⁨8⁩ ⁨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.

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    • MBM@lemmings.world ⁨8⁩ ⁨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.

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      • CowsLookLikeMaps@sh.itjust.works ⁨8⁩ ⁨months⁩ ago

        Oh, sorry about that! Your cheekiness went right over my head. 😋

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  • DaleGribble88@programming.dev ⁨8⁩ ⁨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.

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    • MBM@lemmings.world ⁨8⁩ ⁨months⁩ ago

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

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