Busy Beaver Hunters Reach Numbers That Overwhelm Ordinary Math

Re:Busy Beaver Hunters Reach Numbers That Overwhelm Ordinary... by brap on Monday August 25, 2025 @02:08AM (#45010737)

At some point you gotta wonder if there’s even a difference between “stops after N” and “never stops”.

I mean obviously there is, it’s the same difference between N and infinity. But… is there really?

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Re:Busy Beaver Hunters Reach Numbers That Overwhelm Ordinary... by lanternfish on Monday August 25, 2025 @03:09AM (#45011136)

In a mathematical sense - absolutely. You can dual halting problem against many very tangible qualities - like whether a (proved) statement is true or false. A (large-n) halting program is closer to an instantly halting program not just because n is always closer to 0 than inf, but because 'large n halting' and 'instantly halting' are ontologically similar in a way they just aren't with unhalting programs.

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Re:Busy Beaver Hunters Reach Numbers That Overwhelm Ordinary... by dwohnitmok on Monday August 25, 2025 @03:06AM (#45011114)

Welcome to ultrafinitism!

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Re:Busy Beaver Hunters Reach Numbers That Overwhelm Ordinary... by fuckaj on Monday August 25, 2025 @07:43AM (#45012780)

Well since we got off the Gold standard, we might need those big numbers.

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