Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
A more consistent definition of tetration of tetration for rational exponents
#6
GFR Wrote:I have examined with interest the "details" shown in the UVIR's posting. Unfortunately, I cannot agree with putting:
b # n = y => b = y # (1/n).

Quote:There has already been at least one peer reviewed paper on this definition of tetraroots, so whether you "agree" or not is irrelevant.

The tetra root is defined as the inverse of the x#n but it has nothing to do with x#(1/n).


GFR Wrote:Moreover, I think that these two "tetration" formulas don't have any point in common. Their sets are disjoint. There is no similarity with the "exponentiation" case, where the power and the root functions are described in the same domain and we can find a root function representable as a power. I know but, unfortunately, ... this is the real problem.

I absolutely agree with Gianfranco.
The reason why and coincide is that . If we demand this law to be valid also for rational exponents then and thatswhy must be the inverse of . Unfortunately is no more valid.

Quote:The tetraroot is the exact reverse operation of tetration, since
Nobody denies that the tetraroot is the inverse of (by definition) however to define as being the tetraroot is quite arbitrary and additionally does not coincide with our other methods. As far as I have seen the 3 definitions of (via Daniel's continuous iteration at the first fixed point, via Gottfried's matrixoperator method and via Andrew's natural slog) coincide for . As an example I graphed (via the method of continuous iteration at the first fixed point) (red) in comparison with the inverse of (blue):

   
Curve 1 is
Curve 2 is the identity function.
Curve 3 is and
Curve 4 is the inverse of (2nd superroot)

Quote:

Sorry Ioannis, but this rather proves that it is the wrong definition. As should be a function continuous in it must
Reply


Messages In This Thread
RE: A more consistent definition of tetration of tetration for rational exponents - by bo198214 - 09/30/2007, 06:18 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Tetration research: 1986 - 1991 Daniel 0 175 03/20/2020, 02:47 AM
Last Post: Daniel
  umbral and tetration tetration101 3 373 03/02/2020, 06:28 AM
Last Post: Daniel
  tetration from alternative fixed point sheldonison 22 32,221 12/24/2019, 06:26 AM
Last Post: Daniel
  Constructing real tetration solutions Daniel 4 996 12/24/2019, 12:10 AM
Last Post: sheldonison
  Thoughts on hyper-operations of rational but non-integer orders? VSO 2 950 09/09/2019, 10:38 PM
Last Post: tommy1729
  I need somebody to help me clarifiy the elementary knowledge for tetration Ember Edison 13 5,060 08/26/2019, 01:44 PM
Last Post: Ember Edison
  Complex Tetration, to base exp(1/e) Ember Edison 7 3,031 08/14/2019, 09:15 AM
Last Post: sheldonison
  Minimum axioms to extend tetration Daniel 0 569 07/21/2019, 11:38 AM
Last Post: Daniel
  Critic of Tetration.org Daniel 2 1,083 07/21/2019, 01:32 AM
Last Post: Daniel
  Dimesional analysis and tetration tetration101 1 1,073 06/23/2019, 08:43 PM
Last Post: Chenjesu



Users browsing this thread: 1 Guest(s)