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BusyBeaver(6) Is Quite Large

(scottaaronson.blog)
271 points bdr | 1 comments | 28 Jun 25 16:53 UTC | HN request time: 0.27s | source
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Scarblac ◴[28 Jun 25 17:29 UTC] No.44406478[source]▶
It boggles my mind that a number (an uncomputable number, granted) like BB(748) can be "independent of ZFC". It feels like a category error or something.
replies(12): >>44406574 #>>44406590 #>>44407165 #>>44407378 #>>44407396 #>>44407448 #>>44407506 #>>44407549 #>>44408495 #>>44409048 #>>44410736 #>>44413092 #
ChadNauseam ◴[28 Jun 25 17:37 UTC] No.44406574[source]▶
The number itself is not independent of ZFC. (Every integer can be expressed in ZFC.) What's independent of ZFC is the process of computing BB(748).
replies(3): >>44406611 #>>44407419 #>>44407440 #
Straw ◴[28 Jun 25 17:41 UTC] No.44406611[source]▶
Sure, if someone just gives you the number, ZFC can represent it. But ZFC cannot prove that the value is correct, so how do you know you have the right number? Use a stronger proof system? Go a bit bigger and same issue.
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1. vhcr ◴[29 Jun 25 05:10 UTC] No.44410514[source]▶
Nobody can give you that number, because it's way bigger than what can be represented in the universe.