• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 The super 0th root and a new rule of tetration? sheldonison Long Time Fellow Posts: 641 Threads: 22 Joined: Oct 2008 11/28/2017, 04:15 PM (This post was last modified: 11/28/2017, 09:28 PM by sheldonison.) (11/27/2017, 06:33 PM)Xorter Wrote: Okay, I revised the formula, and I guess my intuation mislead me, maybe. But I have a good news, too. Maybe this formula will bring the trueth: lim h->infinity (log(f(x+1/h)^^N)/log(f(x)^^N))^^h = lim h->infinity ((log(f(x+1/h))/log(f(x)))^^h)^^N Do you think it can be correct? I can't understand the formula, but one question is why have f(x) as opposed to x?  Are you trying to iterate f(x)???   Also one assumes you are only interested in this limit for exp(-e)<=a<=exp(1/e),  $\lim_{h\to\infty}a\uparrow\uparrow h$  otherwise it is not defined.  if  exp(-e)<=a<=exp(1/e), then it is the real attracting fixed point of a^L=L.  Is this a correct understanding of your intentions? update: Also, the 1/h terms in your equation drop out as h->infinity.  Then you have:                 (log(x^^N)/log(x^^N))^^h = ((log(x)/log(x))^^h)^^N The ^^h is interpreted as the attracting fixed point.  The attracting fixed point of a^^infty as a approaches 1 also approaches a:  fixed(a^^infity) ~=  a + (a-1)^2 + O(a-1)^3, So the numerators equal the denominators and we are left with 1 = 1 - Sheldon « Next Oldest | Next Newest »

 Messages In This Thread The super 0th root and a new rule of tetration? - by Xorter - 11/27/2017, 01:44 PM RE: The super 0th root and a new rule of tetration? - by Xorter - 11/27/2017, 06:33 PM RE: The super 0th root and a new rule of tetration? - by sheldonison - 11/28/2017, 04:15 PM RE: The super 0th root and a new rule of tetration? - by Xorter - 11/28/2017, 05:45 PM RE: The super 0th root and a new rule of tetration? - by Xorter - 11/29/2017, 11:53 AM

 Possibly Related Threads... Thread Author Replies Views Last Post Is bugs or features for fatou.gp super-logarithm? Ember Edison 10 5,926 08/07/2019, 02:44 AM Last Post: Ember Edison A fundamental flaw of an operator who's super operator is addition JmsNxn 4 8,268 06/23/2019, 08:19 PM Last Post: Chenjesu Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 6,595 06/10/2019, 04:29 AM Last Post: Ember Edison Inverse super-composition Xorter 11 16,172 05/26/2018, 12:00 AM Last Post: Xorter Solving tetration using differintegrals and super-roots JmsNxn 0 2,362 08/22/2016, 10:07 PM Last Post: JmsNxn Cellular auto : rule 30 number ? tommy1729 0 1,646 08/03/2016, 08:31 PM Last Post: tommy1729 The super of exp(z)(z^2 + 1) + z. tommy1729 1 3,193 03/15/2016, 01:02 PM Last Post: tommy1729 Super-root 3 andydude 10 13,468 01/19/2016, 03:14 AM Last Post: andydude [rule 30] Is it possible to easily rewrite rule 30 in terms of modular arithmetic ? tommy1729 0 1,951 07/24/2014, 11:09 PM Last Post: tommy1729 super of exp + 2pi i ? tommy1729 1 3,963 08/18/2013, 09:20 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)