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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: 0.22s | 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 #
1. LegionMammal978 ◴[28 Jun 25 19:22 UTC] No.44407396[source]▶
Let X = "1 if ZF is consistent, 0 otherwise". Then the statements "X = 0" and "X = 1" are independent of ZF. Whether the definition of X is a satisfactory definition of a particular number is a question of mathematical philosophy.

BB(748) is very similar, in that I'd call it a 'definition' independent of ZF rather than a 'number' independent of ZF.