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open problems survey
#8
Conjecture
The following holds for regular tetration:
for all and 0 < |y| < 1.
The following holds for intuitive tetration:
for all and 0 < |y| < 1.

Discussion
This would be interesting in its own right, partly because it is symmetric, but also because it is useful in demonstrating the difference between reciprocal heights and super-roots. Another notable aspect of this set of bounds is that it is very extension-dependent. This does not hold for linear tetration.

Appended are several graphs of the function for x = 1.001, 1.1, eta, e, 10. The first three (1.001, 1.1, eta) were calculated with regular tetration, and the last two (e, 10) were calculated with intuitive tetration. More discussion of this is here


Attached Files
.pdf   xty-times-xtny-base-1p001.pdf (Size: 6.39 KB / Downloads: 451)
.pdf   xty-times-xtny-base-1p1.pdf (Size: 6.28 KB / Downloads: 445)
.pdf   xty-times-xtny-base-eta.pdf (Size: 6.26 KB / Downloads: 417)
.pdf   xty-times-xtny-base-e.pdf (Size: 6.2 KB / Downloads: 429)
.pdf   xty-times-xtny-base-10.pdf (Size: 6.31 KB / Downloads: 421)
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Messages In This Thread
open problems survey - by bo198214 - 05/17/2008, 10:03 AM
Exponential Factorial, TPID 2 - by andydude - 05/26/2008, 03:24 PM
Existence of bounded b^z TPID 4 - by bo198214 - 10/08/2008, 04:22 PM
A conjecture on bounds. TPID 7 - by andydude - 10/23/2009, 05:27 AM
Logarithm reciprocal TPID 9 - by bo198214 - 07/20/2010, 05:50 AM
RE: open problems survey - by nuninho1980 - 10/31/2010, 09:50 PM
Tommy's conjecture TPID 16 - by tommy1729 - 06/07/2014, 10:44 PM
The third super-root TPID 18 - by andydude - 12/25/2015, 06:16 AM

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