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 Tetration is pentation. This deserve more thinking. marraco Fellow Posts: 100 Threads: 12 Joined: Apr 2011 03/30/2015, 02:54 PM (This post was last modified: 03/30/2015, 04:14 PM by marraco.) Observe this incredible sequence $\vspace{15}{(a)\^\^a = a^{a-1} = N_a\,^{a^a} \,=\, N_a\,^{N_a\,^{a^2}} \,=\, N_a\,^{N_a\,^{N_a\,^{2a}}} \,=\, N_a\,^{N_a\,^{N_a\,^{N_a\,^{ln_{a}(2^a)+a}}}} \,=\, ... }$ This hints that the zeration $\vspace{15}{a\circ a=ln_{N_a}(2)+a }$, which is even another argument in favor of $\vspace{15}{a\circ b=ln_{?}(?^a+?^b) }$, but also hints about what is below zeration, and maybe it can explored over tetration. -Is trivial that the former sequence of towers converge to $\vspace{15}{ a^{a-1} }$. -Is puzzling that the exponent (2+a) is missing. « Next Oldest | Next Newest »

 Messages In This Thread Tetration is pentation. This deserve more thinking. - by marraco - 03/30/2015, 12:30 PM RE: Tetration is pentation. This deserve more thinking. - by marraco - 03/30/2015, 12:43 PM RE: Tetration is pentation. This deserve more thinking. - by marraco - 03/30/2015, 02:54 PM

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