Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
A more consistent definition of tetration of tetration for rational exponents
#8
UVIR Wrote:
bo198214 Wrote:Nobody denies that the tetraroot is the inverse of (by definition) however to define as being the tetraroot is quite arbitrary

Why? What is "arbitrary" about it? And if it's "arbitrary", in what "sense" is it "arbitrary"?

It is in the same sense arbitrary as say that I define
. No rule justifies that should be the inverse of .
If you not even demand that is continuous, what will then remain?

Quote:Again, if the definition of the n-th order tetraroot as is "arbitrary", surely the tetraroot can be defined better as for some m,n. Do you care to define m and n in some other consistent way for the tetraroot?

The n-th tetraroot is already clearly defined as the inversion of , no need to redefine it. What we all are seeking for is a sound definition for the tetration for non-integer exponents. Natural demands are being analytic, strict increase and .

Quote:So? Has a divine judge decided on the validity of any of the proposed methods so far?

The interesting thing is not about validity of each single method, but rather that 3 completely different methods yield identical values.

Quote:So, if you tell me for example, take Andrew's or Gottfried's or your method and "input" 0.666... or 0.6363..., and then see what the function outputs, this is already suffering badly as a definition.

Can not see how this suffers.
Take for example the method of continuous iteration at a fixed point.
There you move the fixed point of to 0, say where a is the fixed point of .
Then you compute by unique analytic solution of the equation and then you have the value
.
Reply


Messages In This Thread
RE: A more consistent definition of tetration of tetration for rational exponents - by bo198214 - 09/30/2007, 08:06 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 1,082 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)