Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Tetration is pentation. This deserve more thinking.
#1
Possibly iterated left bracket tetration has a way to solve real exponents of right bracket tetration.

Here the bracket shows the place where, the result of the last iteration, is placed on the next iteration.
Common tetration is right bracket, and the weak alternative is left bracket:



where

Note that

Let be
And in general, n iterations: this is actually a form of weak pentation, because is an iteration of a weak form of tetration.

In some sense, tetration is a form of pentation, and we are trying to solve a pentation without understanding his base tetration.

Note that if we solve this iteration for , we also solve tetration to any real exponents.
Reply
#2
An alternative form is


then


also:

Reply
#3
Observe this incredible sequence



This hints that the zeration , which is even another argument in favor of , 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 .
-Is puzzling that the exponent (2+a) is missing.
Reply


Possibly Related Threads...
Thread Author Replies Views Last Post
  pentation and hexation sheldonison 9 11,499 09/18/2019, 02:34 PM
Last Post: sheldonison
  [2015] 4th Zeration from base change pentation tommy1729 5 7,309 03/29/2015, 05:47 PM
Last Post: tommy1729
  Mizugadro, pentation, Book Kouznetsov 41 57,473 03/02/2015, 08:13 PM
Last Post: sheldonison
  New thinking about math infinity MikeSmith 0 3,221 10/14/2013, 11:18 AM
Last Post: MikeSmith
  Infinite Pentation (and x-srt-x) andydude 20 30,653 05/31/2011, 10:29 PM
Last Post: bo198214
  Regular "pentation"? mike3 12 23,913 04/04/2011, 03:16 AM
Last Post: BenStandeven
Smile Pentation roots self but please you do... nuninho1980 2 7,806 11/03/2010, 12:54 PM
Last Post: nuninho1980
  Pentation's definitional ambiguity Base-Acid Tetration 14 25,292 12/15/2009, 11:23 PM
Last Post: Base-Acid Tetration
  Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation Base-Acid Tetration 19 35,175 10/24/2009, 04:12 AM
Last Post: andydude
  Exploring Pentation - Base e jaydfox 22 42,797 03/03/2008, 08:04 PM
Last Post: Ivars



Users browsing this thread: 1 Guest(s)