Pleroma

is there a (useful) finite number that is so big we haven't been able to formulate an upper bound for it?

@SuricrasiaOnline Rayo's number is not useful but it's very big

@SuricrasiaOnline Busy beaver numbers come to mind. There is no computable function f such that f(n) > BB(n) for all n.

@SuricrasiaOnline When you start invoking Ackerman functions or chained-arrow notation I tend to assume we've left the realm of "(useful)", so I'm going to go with "no", but I'm sure there are grad students who would disagree.

@SuricrasiaOnline
It depends how good you are in math.
In my case that's close to 241.
Once i counted to 238 and i'm pretty sure this algorithm could continue at least to 241 but not much.
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