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 The super 0th root and a new rule of tetration? Xorter Fellow Posts: 90 Threads: 29 Joined: Aug 2016 11/28/2017, 05:45 PM (11/28/2017, 04:15 PM)sheldonison Wrote: 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? Well, first of all, f(x) is any function, it can be x^2+3, cos(x), x, ... etc. No, I have not tried iterate f(x) (functionally like f^oN), because these formulas are based on the iteration of addition (multiplication, exponentiation,...etc.), but I could try it, why not? In fact it is not the lim h->infinity a^^h, because that is equals to W(-ln(a))/-ln(a). I have been looking for lim h->0 super h-th root of a. You know, x^^(1/y) is not super y-th root of x, right? This is my big problem, but I believe it might be our advantage. Xorter Unizo « 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

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