←back to thread

BusyBeaver(6) Is Quite Large

(scottaaronson.blog)
271 points bdr | 1 comments | 28 Jun 25 16:53 UTC | HN request time: 0.291s | source
Show context
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 #
LPisGood ◴[28 Jun 25 23:29 UTC] No.44409048[source]▶
BB(748) is a natural number, and _all_ natural numbers are computable.
replies(1): >>44410922 #
1. ted_dunning ◴[29 Jun 25 07:12 UTC] No.44410922[source]▶
There is definitely a function f such that f() = n for all n ∈ ℕ.

But there is also a function g that you cannot prove whether g() = n.

Important distinction.

This means that somebody could claim that the value of BB(748) = n but you cannot be sure if they are correct (but you might be able to show they are wrong).