• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Zeration = inconsistant ? tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 10/04/2014, 10:20 PM (This post was last modified: 10/04/2014, 10:25 PM by tommy1729.) Example : Solve exp^[2]( 2 ln^[2](x) ) = 7 This is equivalent to x^ln(x) = 7. Take some real a,b >= exp(1). a_0 = a^{ 1 / ln(b) } b_0 = 7^{ ln(b) / ln(a) } replacement rules : --- a ' = a * 7^{ ln(b) } b ' = a * b --- a_1 = a ' ^{ 1/ln(b ') } b_1 = 7^{ ln(b ') / ln(a ') } repeat forever lim n-> oo a_n/b_n = x. this gives x = exp( sqrt( ln(7) ) ) as it should. Numerically we get x = 4.0348084730118923250275859453110072467762717139110... Notice 1/x is also a solution. If we take 0 < a,b < 1/exp(1) ( =exp(-1) ) we probably achieve that. This numerical algorithm can probably be improved with adding some + operators at the right places ... Still investigating. Notice I did not use a derivative anywhere like most numerical methods do. Also the method can probably be extended nicely to all interpretations of hyperoperators. Extending towards complex numbers however seems difficult. (unless we split up by variables for real and imag part ) Can zeration inprove this algoritm ? regards tommy1729 " So he can probably do math better than most cows , so what ? " Ullrich mocking me on sci.math. " Truth is that what does not go away when you stop believing in it " tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread Zeration = inconsistant ? - by tommy1729 - 10/01/2014, 08:40 AM RE: Zeration = inconsistant ? - by MphLee - 10/01/2014, 11:27 AM RE: Zeration = inconsistant ? - by GFR - 10/02/2014, 02:44 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 09:27 PM RE: Zeration = inconsistant ? - by MphLee - 10/02/2014, 10:02 PM RE: Zeration = inconsistant ? - by GFR - 10/04/2014, 09:58 AM RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 10:58 PM RE: Zeration = inconsistant ? - by GFR - 10/03/2014, 11:29 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:11 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 11:11 PM RE: Zeration = inconsistant ? - by GFR - 10/03/2014, 11:39 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:12 PM RE: Zeration = inconsistant ? - by MphLee - 10/03/2014, 09:20 AM RE: Zeration = inconsistant ? - by tommy1729 - 10/03/2014, 09:32 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/03/2014, 09:41 PM RE: Zeration = inconsistant ? - by GFR - 10/04/2014, 10:19 AM RE: Zeration = inconsistant ? - by MphLee - 10/04/2014, 11:24 AM RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:16 PM RE: Zeration = inconsistant ? - by MphLee - 10/04/2014, 12:58 PM RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 10:20 PM RE: Zeration = inconsistant ? - by MphLee - 10/05/2014, 03:36 PM

 Possibly Related Threads... Thread Author Replies Views Last Post Zeration GFR 80 106,029 10/31/2016, 02:57 PM Last Post: Stanislav Zeration reconsidered using plusation. tommy1729 1 3,048 10/23/2015, 03:39 PM Last Post: MphLee Is this close to zeration ? tommy1729 0 2,100 03/30/2015, 11:34 PM Last Post: tommy1729 [2015] 4th Zeration from base change pentation tommy1729 5 5,996 03/29/2015, 05:47 PM Last Post: tommy1729 [2015] New zeration and matrix log ? tommy1729 1 3,266 03/24/2015, 07:07 AM Last Post: marraco [2014] Inconsistant equation ? tommy1729 0 1,827 07/27/2014, 02:38 PM Last Post: tommy1729 base change inconsistant ? tommy1729 2 3,206 11/26/2012, 08:13 AM Last Post: Nasser

Users browsing this thread: 1 Guest(s)