What grows faster: Busy Beaver function, TREE function or BEAF largest resursive functions (legions, lugions, lagions...)?
closed as off topic by Bugs Bunny, Gjergji Zaimi, Dan Petersen, David Roberts, Bill Johnson Sep 14 '12 at 10:40
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Much too easy for this site, and already answered. Anyway, BusyBeaver grows faster that any computable function (almost by definition); as the other two are computable... (btw, TREE grows inimaginably faster that the recursive functions you cite next). All these questions tend to show that you have not studied the http://en.wikipedia.org/wiki/Fastgrowing_hierarchy>fastgrowing hierarchy : in this notation, Conway's $n\rightarrow n \rightarrow\dots\rightarrow n$ (with $n$ arrows) is (much) smaller than $f_{\omega^2+1}(n)$, and any "recursive" construction in the line of BEAF grows slower than $f_{\omega^\omega}$, while TREE grows much faster than $f_{\epsilon_0}$, or even $f_{\Gamma_0}$... 

