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 nextnext). 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 $f_{\Gamma_0}$...
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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) |
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