Comment by 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?
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?
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.
(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.)
Proving BB(748)=X for some concrete X in ZFC is equivalent to proving Con(ZFC) in ZFC.
Yes, but I'm not "proving BB(748)=X in ZFC" in my previous comment.
I clearly stated:
> as long as we assume ZFC is consistent
In other words, I'm talking about proving BB(748)=X in ZFC+Con(ZFC), which is not fundamentally impossible. It's practically impossible simply because you need to reason out the sheer amount of TMs with 748 states.
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