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Tetration FAQ Discussion
#9
@Gottfried
Oh, about your top-down towers as opposed to bottom up towers, I've put some thought into those as well, and I've come up with a notation for those based on Barrow/Shell's tower notation.



This way of looking at it makes it not so much a matter of notation (as yours is) but a matter of indexing. The reversed indexing allows you to take the limit in the other direction as I think you were talking about. Also using this notation, your downward towers can be written:



My only worry with this kind of tower is that the limits will be found to always evaluate to and will not provide a very "rich" convergence landscape.

Andrew Robbins

PS. I also find it interesting that the "k=1" at the top of the big-T fits on the line of the T which is bigger and the "n" fits at the bottom of the T which is smaller, so the top-down notation fits better with the T notation, just as the top-down view of nested exponentials is how they are actually evaluated, bringing us closer to reality.
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Messages In This Thread
Tetration FAQ Discussion - by bo198214 - 08/09/2007, 12:07 AM
Literature - by Gottfried - 11/23/2007, 04:30 PM
RE: Literature - by andydude - 12/17/2007, 07:31 PM
RE: Tetration FAQ - by andydude - 01/13/2008, 08:43 AM
RE: Tetration FAQ - by Ivars - 01/13/2008, 10:17 AM
RE: Tetration FAQ - by GFR - 01/13/2008, 04:02 PM
RE: Tetration FAQ - by andydude - 01/16/2008, 04:13 AM
RE: Tetration FAQ Discussion - by Gottfried - 07/17/2008, 10:34 AM
FAQ-discuss: What is a fixpoint? - by Gottfried - 07/17/2008, 10:45 AM
FAQ-discuss: What does f o g mean? - by Gottfried - 07/17/2008, 10:47 AM
Intro and Formula sheet - by andydude - 11/13/2007, 01:21 AM
RE: Intro and Formula sheet - by jaydfox - 11/13/2007, 02:39 AM
RE: Intro and Formula sheet - by andydude - 11/13/2007, 03:15 AM
RE: Intro and Formula sheet - by andydude - 11/13/2007, 03:25 AM
RE: Intro and Formula sheet - by Gottfried - 11/13/2007, 06:08 AM
RE: Intro and Formula sheet - by Gottfried - 11/13/2007, 06:12 AM
RE: Intro and Formula sheet - by andydude - 11/13/2007, 08:37 AM
RE: Intro and Formula sheet - by andydude - 11/13/2007, 09:09 AM
RE: Intro and Formula sheet - by bo198214 - 11/13/2007, 10:42 AM
RE: Intro and Formula sheet - by andydude - 11/15/2007, 03:16 AM
RE: Intro and Formula sheet - by jaydfox - 11/15/2007, 03:38 AM
RE: Intro and Formula sheet - by andydude - 11/30/2007, 05:32 PM
[split] Tetration FAQ - by Ivars - 07/11/2008, 06:28 AM

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