Thread Rating:
  • 1 Vote(s) - 3 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Functional super-iteration and hierarchy of functional hyper-iterations
(05/03/2009, 07:21 PM)Tetratophile Wrote: For the function x -> x+1, you simply hyper-n-iterate the function f x0+1 times at x=x0, (eg. at x=2 you iterate 3 times, and at x=3.5 you iterate 4.5 times etc.) So I don't think that a non-constant function in the second argument would behave differently from a constant function in this respect.

If we take the equations as recursive definitions then is only defined for functions in the second argument that are constant. Thatswhy I proposed the different version.

Quote:Also would not be true, because at n=0,

Ok, I also made another mistake in the previous posting, so here again the recursive definition



From that follows


Messages In This Thread
RE: Functional super-iteration and hierarchy of functional composition-based operations - by bo198214 - 05/03/2009, 08:13 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Thoughts on hyper-operations of rational but non-integer orders? VSO 2 156 09/09/2019, 10:38 PM
Last Post: tommy1729
  [MSE] Shape of orbit of iterations with base b on Shell-Thron-region Gottfried 3 354 08/18/2019, 02:22 PM
Last Post: sheldonison
  Is bugs or features for super-logarithm? Ember Edison 10 1,152 08/07/2019, 02:44 AM
Last Post: Ember Edison
  A fundamental flaw of an operator who's super operator is addition JmsNxn 4 6,204 06/23/2019, 08:19 PM
Last Post: Chenjesu
  Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 1,607 06/10/2019, 04:29 AM
Last Post: Ember Edison
  Inverse super-composition Xorter 11 11,445 05/26/2018, 12:00 AM
Last Post: Xorter
  Math overflow question on fractional exponential iterations sheldonison 4 3,079 04/01/2018, 03:09 AM
Last Post: JmsNxn
  The super 0th root and a new rule of tetration? Xorter 4 3,315 11/29/2017, 11:53 AM
Last Post: Xorter
  Hyper-volume by integration Xorter 0 1,224 04/08/2017, 01:52 PM
Last Post: Xorter
  Functional power Xorter 0 1,149 03/11/2017, 10:22 AM
Last Post: Xorter

Users browsing this thread: 1 Guest(s)