• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Rational operators (a {t} b); a,b > e solved JmsNxn Long Time Fellow Posts: 739 Threads: 104 Joined: Dec 2010 06/08/2011, 04:54 AM (06/07/2011, 06:59 AM)bo198214 Wrote: You mean "triation". Its greek numbering not latin Actually I agree with you, in certain contexts I worked with it also seems more suitable to use addition as operation 0. (Even Ackermann did so.) On the other hand, on different contexts there it seems more preferable to start with 1. E.g. to have the zero-th operation a [0] x = x+1. And I dont think one can roll back the whole historic naming development, tetration, the forth operation is already ingrained in the minds. I'm glad you agree with me about centering $\vartheta$ with addition as zero. I actually originally centered it at zero because Ackermann did. triation sounds nicer than tertiation. But besides this, I have something to report. $\lim_{y\to\infty}\vartheta(a, b, x\pm iy) = L$ which converges absolutely for all $a,b \in C$ and $x \in (-\infty, 2]$. Interestingly enough L does not change with a and b and seems to be only x dependent. L seems to always be greater than 2.6 but just around it. At first I thought it was a universal constant they were all converging to, but only $x \in [0, 0.5]$ showed convergence to this value. « Next Oldest | Next Newest »

 Messages In This Thread Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/06/2011, 02:45 AM RE: Rational operators (a {t} b); a,b > e solved - by sheldonison - 06/06/2011, 04:39 AM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/06/2011, 05:34 AM RE: Rational operators (a {t} b); a,b > e solved - by sheldonison - 06/06/2011, 06:02 AM RE: Rational operators (a {t} b); a,b > e solved - by sheldonison - 06/06/2011, 07:03 AM RE: Rational operators (a {t} b); a,b > e solved - by nuninho1980 - 06/06/2011, 05:16 PM RE: Rational operators (a {t} b); a,b > e solved - by bo198214 - 06/06/2011, 06:53 AM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/06/2011, 08:47 AM RE: Rational operators (a {t} b); a,b > e solved - by bo198214 - 06/06/2011, 09:23 AM RE: Rational operators (a {t} b); a,b > e solved - by tommy1729 - 06/06/2011, 11:59 AM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/06/2011, 05:44 PM RE: Rational operators (a {t} b); a,b > e solved - by bo198214 - 06/06/2011, 09:28 PM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/06/2011, 07:47 PM RE: Rational operators (a {t} b); a,b > e solved - by sheldonison - 06/06/2011, 08:43 PM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/07/2011, 02:45 AM RE: Rational operators (a {t} b); a,b > e solved - by bo198214 - 06/07/2011, 06:59 AM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/08/2011, 04:54 AM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/08/2011, 07:31 PM RE: Rational operators (a {t} b); a,b > e solved - by sheldonison - 06/08/2011, 08:32 PM RE: Rational operators (a {t} b); a,b > e solved - by bo198214 - 06/08/2011, 09:14 PM RE: Rational operators (a {t} b); a,b > e solved - by tommy1729 - 09/02/2016, 01:50 AM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/08/2011, 11:47 PM RE: Rational operators (a {t} b); a,b > e solved - by Gottfried - 06/11/2011, 02:33 PM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/12/2011, 07:55 PM RE: Rational operators (a {t} b); a,b > e solved - by Xorter - 08/21/2016, 06:56 PM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 08/22/2016, 12:36 AM RE: Rational operators (a {t} b); a,b > e solved - by Xorter - 08/24/2016, 07:24 PM RE: Rational operators (a {t} b); a,b > e solved - by Xorter - 08/29/2016, 02:06 PM RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 09/01/2016, 06:47 PM RE: Rational operators (a {t} b); a,b > e solved - by tommy1729 - 09/02/2016, 02:04 AM RE: Rational operators (a {t} b); a,b > e solved - by tommy1729 - 09/02/2016, 02:11 AM

 Possibly Related Threads… Thread Author Replies Views Last Post The $$\varphi$$ method of semi operators, the first half of my research JmsNxn 7 181 Yesterday, 11:57 PM Last Post: JmsNxn The bounded analytic semiHyper-operators JmsNxn 4 7,433 Yesterday, 11:46 PM Last Post: JmsNxn Thoughts on hyper-operations of rational but non-integer orders? VSO 3 4,323 06/28/2022, 08:33 AM Last Post: Catullus Holomorphic semi operators, using the beta method JmsNxn 71 3,808 06/13/2022, 08:33 PM Last Post: JmsNxn [MSE-SOLVED] Subfunction is functorial!!!! MphLee 14 5,438 06/06/2021, 11:16 PM Last Post: JmsNxn Hyper operators in computability theory JmsNxn 5 10,555 02/15/2017, 10:07 PM Last Post: MphLee Recursive formula generating bounded hyper-operators JmsNxn 0 3,593 01/17/2017, 05:10 AM Last Post: JmsNxn holomorphic binary operators over naturals; generalized hyper operators JmsNxn 15 30,570 08/22/2016, 12:19 AM Last Post: JmsNxn Bounded Analytic Hyper operators JmsNxn 25 42,412 04/01/2015, 06:09 PM Last Post: MphLee Incredible reduction for Hyper operators JmsNxn 0 4,172 02/13/2014, 06:20 PM Last Post: JmsNxn

Users browsing this thread: 1 Guest(s)