What grows faster? - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-06-19T17:27:32Z http://mathoverflow.net/feeds/question/107155 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/107155/what-grows-faster What grows faster? Ikosarakt 2012-09-14T08:34:50Z 2012-09-14T10:18:18Z <p>What grows faster: Busy Beaver function, TREE function or BEAF largest resursive functions (legions, lugions, lagions...)?</p> http://mathoverflow.net/questions/107155/what-grows-faster/107160#107160 Answer by Feldmann Denis for What grows faster? Feldmann Denis 2012-09-14T09:39:04Z 2012-09-14T10:00:54Z <p>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 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 $f_{\Gamma_0}$... </p>