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Michael Richardson: Brian 2 is right -- Busy Beaver bb(n) grows faster than Ackermann or any other computable function f(n).
Wrong! There is no evidence to conclude that the Ackermann function is slower growing than the Busy Beaver Sigma.
The fact that a function is not computable doesn't necessarily mean it needs to be fast growing (e.g. convert the halting problem to a function that returns a boolean: not very fast growing, is it?)
Ackermann function is a computable function and for any computable function f(BBSigma(n)) < BBSigma(n+1).
Bill is right about there being no evidence that the Ackermann function grows slower than a non-computable function in general, but for the busy beaver function there is a proof that it grows faster than any computable function. See the wikipedia article for a proof.
(why do I need your e-mail?)
It would be nice if you left your e-mail address. Sometimes I want to send a private message, or just thank for the great comment. Having your e-mail really helps.
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(Your twitter handle, if you have one.)
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