# What grows faster? [closed]

What grows faster: Busy Beaver function, TREE function or BEAF largest resursive functions (legions, lugions, lagions...)?

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## closed as off topic by Bugs Bunny, Gjergji Zaimi, Dan Petersen, David Roberts, Bill JohnsonSep 14 '12 at 10:40

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## 1 Answer

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/Fast-growing_hierarchy>fast-growing 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 $f_{\Gamma_0}$...

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For now, I studied FGH and figured out that TREE(n) surpasses $f_{\vartheta(\Omega^\omega)}(n)$. –  Ikosarakt May 15 '13 at 23:02