Fast-Growing Hierarchy

No.11178259 ViewReplyOriginalReport
Is Busy Beaver faster than any computable sequence?
Is it really impossible to construct and evaluate a faster growing function? Sure, maybe knowing exact value of BB(n) for any arbitrary n would cause halting paradox, but why can't we just continue to came up with new limit ordinals, diagonalize fast growing function until we reach Busy Beaver speed of growth?