Comment by raincole

8 months ago

BB(748) is a finite number, but I'd argue its magic also comes from infinites: the fact some Turing Machines run forever and never halt.

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raincole

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joelthelion  8 months ago

Is it? If it's not possible to prove that it's the best solution to bb(748), does it even exist in any meaningful way?

  • raincole  8 months ago

    I'm not sure what you mean. First of all BB(n) is a function so it has value(s).

    And in theory we can prove BB(748)=X, where X is a plain big natural number, as long as we just assume ZFC is consistent. It's practically impossible, but not fundamentally impossible like proving Con(ZFC) in ZFC itself.

    • raincole  8 months ago

      (Late Edit: the above comment was rather sloppy. I meant that we don't know if it's impossible to prove BB(748)=X in ZFC+Con(ZFC). It's not necessarily possible either. We just haven't ruled out the possibility.)