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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: 0.241s | 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.
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Straw ◴[28 Jun 25 17:39 UTC] No.44406590[source]▶
The category error is in thinking that BB(748) is in fact, a number. It's merely a mathematical concept.
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1. gylterud ◴[28 Jun 25 19:04 UTC] No.44407244[source]▶
A constructive mathematician would indeed deny that BB(748) is a well defined number. One could define it as a predicate on natural numbers, but lest we find a contradiction in ZFC we cannot hope to constructively prove that it holds for any number.