Thread Rating:
  • 1 Vote(s) - 1 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Tetration extension for bases between 1 and eta
(11/07/2009, 11:30 PM)dantheman163 Wrote: If we set which is to say

then reduce it to

Then just strait up plug in infinity for k
we get which is the same as

Slowly, slowly. The first line is what you want to show. You show from the first line something true, but you can also show something true starting from something wrong; so thats not sufficient. Also it seems as if you confuse limit equality with sequence equality.

Lets have a look at the inverse function ,
it should satisfy

Then lets compute

Take for example then the right side converges to the derivative of at the fixed point; and not to 1 as it should be.

This is the reason why the formula is only valid for functions that have derivative 1 at the fixed point, e.g. , i.e. .

Quote:This is really weird because if i do for
i get about 1.558 which is substantially larger then

Can anyone else confirm that for ?

Try the same with and it will work; but for no other base; except you use the modified formula I described before.

Messages In This Thread
RE: Tetration extension for bases between 1 and eta - by bo198214 - 11/08/2009, 02:44 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Possible continuous extension of tetration to the reals Dasedes 0 1,494 10/10/2016, 04:57 AM
Last Post: Dasedes
  Andrew Robbins' Tetration Extension bo198214 32 46,420 08/22/2016, 04:19 PM
Last Post: Gottfried
  Why bases 0<a<1 don't get love on the forum? marraco 20 18,928 04/19/2015, 05:53 PM
Last Post: Gottfried
  Bundle equations for bases > 2 tommy1729 0 1,977 04/18/2015, 12:24 PM
Last Post: tommy1729
  on constructing hyper operations for bases > eta JmsNxn 1 3,015 04/08/2015, 09:18 PM
Last Post: marraco
  Non-trivial extension of max(n,1)-1 to the reals and its iteration. MphLee 3 4,180 05/17/2014, 07:10 PM
Last Post: MphLee
  extension of the Ackermann function to operators less than addition JmsNxn 2 4,363 11/06/2011, 08:06 PM
Last Post: JmsNxn
  Alternate solution of tetration for "convergent" bases discovered mike3 12 19,360 09/15/2010, 02:18 AM
Last Post: mike3
  my accepted bases tommy1729 0 2,358 08/29/2010, 07:38 PM
Last Post: tommy1729
  [Regular tetration] bases arbitrarily near eta Gottfried 0 2,974 08/22/2010, 09:01 AM
Last Post: Gottfried

Users browsing this thread: 1 Guest(s)