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 Generalized recursive operators Ivars Long Time Fellow Posts: 366 Threads: 26 Joined: Oct 2007 02/02/2008, 10:11 PM andydude Wrote:Wow! I can't believe I gave that away for free! I would pay hundreds to get my hands on this code! Good thing I didn't have to... I just found the asymptotes of pentation, hexation, heptation, octation, and beyond! And they're fascinating:  \begin{align} \lim_{b \rightarrow -2}(a \begin{tabular}{|c|}\hline 4 \\\hline\end{tabular} b) & = -\infty \\ \lim_{b \rightarrow -\infty}(a \begin{tabular}{|c|}\hline 5 \\\hline\end{tabular} b) & = -2 \\ \lim_{b \rightarrow -4}(a \begin{tabular}{|c|}\hline 6 \\\hline\end{tabular} b) & = -\infty \\ \lim_{b \rightarrow -\infty}(a \begin{tabular}{|c|}\hline 7 \\\hline\end{tabular} b) & = -4 \\ \lim_{b \rightarrow -6}(a \begin{tabular}{|c|}\hline 8 \\\hline\end{tabular} b) & = -\infty \\ \lim_{b \rightarrow -\infty}(a \begin{tabular}{|c|}\hline 9 \\\hline\end{tabular} b) & = -6 \end{blign} where the box is GFR's box notation for hyperops, and a is sufficiently close to e, because thats the number I used. I suppose you could see this from the integer versions of these operators, but I think the continuous (or if not continuous, mostly real-valued) versions make it easier to see. Andrew Robbins This is fantastic. Ivars « Next Oldest | Next Newest »

 Messages In This Thread Generalized recursive operators - by Whiteknox - 11/23/2007, 06:42 AM RE: Generalized recursive operators - by bo198214 - 11/23/2007, 08:41 AM RE: Generalized recursive operators - by Whiteknox - 11/23/2007, 03:57 PM RE: Generalized recursive operators - by andydude - 11/25/2007, 01:02 AM RE: Generalized recursive operators - by andydude - 11/29/2007, 04:45 AM RE: Generalized recursive operators - by andydude - 11/29/2007, 05:55 AM RE: Generalized recursive operators - by andydude - 11/29/2007, 06:20 AM RE: Generalized recursive operators - by Gottfried - 11/29/2007, 08:14 AM RE: Generalized recursive operators - by andydude - 11/30/2007, 06:12 PM RE: Generalized recursive operators - by andydude - 11/30/2007, 09:18 PM RE: Generalized recursive operators - by bo198214 - 03/07/2008, 06:58 PM RE: Generalized recursive operators - by Ivars - 02/02/2008, 10:11 PM RE: Generalized recursive operators - by Whiteknox - 12/01/2007, 04:59 AM RE: Generalized recursive operators - by Ivars - 02/03/2008, 10:41 AM RE: Generalized recursive operators - by andydude - 02/11/2008, 09:47 PM RE: Generalized recursive operators - by Ivars - 02/14/2008, 06:05 PM RE: Generalized recursive operators - by GFR - 02/03/2008, 04:12 PM RE: Generalized recursive operators - by Ivars - 02/03/2008, 08:48 PM RE: Generalized recursive operators - by GFR - 02/06/2008, 02:44 PM RE: Generalized recursive operators - by Ivars - 02/06/2008, 02:56 PM RE: Generalized recursive operators - by Ivars - 02/06/2008, 03:43 PM RE: Generalized recursive operators - by GFR - 03/10/2008, 09:53 PM RE: Generalized recursive operators - by GFR - 03/11/2008, 10:24 AM RE: Generalized recursive operators - by bo198214 - 03/11/2008, 10:53 AM RE: Generalized recursive operators - by GFR - 03/12/2008, 12:13 AM RE: Generalized recursive operators - by GFR - 03/13/2008, 06:41 PM RE: Generalized recursive operators - by Stan - 04/04/2011, 11:52 PM

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