• 1 Vote(s) - 5 Average
• 1
• 2
• 3
• 4
• 5
 My favorite integer sequence jaydfox Long Time Fellow Posts: 440 Threads: 31 Joined: Aug 2007 08/09/2014, 11:46 PM (This post was last modified: 08/09/2014, 11:49 PM by jaydfox.) (08/09/2014, 10:52 PM)tommy1729 Wrote: I have the feeling Jay's post/idea is not complete yet or still under development , probably there will be an edit or a followup. A little bit strange notation I think , but that might be due to the unfinished brainstorming too.Yes, still brainstorming, and I'm not attached to any particular notation yet. But I needed something so I could start to formalize... Quote:My first critical remark is that the analogue for exp does not seem convincing right now ; I do not see (1+1/n)^n. But I might need to read again and Jay will probably do an edit or followup. Its just a first impression anyway. (...) I was referring to Jay's post 30 mainly. He posted nr 31 while I made this reply. Take exp_1: Code:k    E_1(k)    E_{1/2}(k)   E_{1/3}(k) 0    1         1            1 1    2         3/2          4/3 2    4         9/4          16/9 3    8         27/4         64/27 exp_1(1) = 2 = (1+1)^1 exp_{1/2}(1) = 2.25 = (1+1/2)^2 exp_{1/3}(1) = 2.370370... = (1+1/3)^3 exp_{1/n}(1) = (1+1/n)^n I could have defined exp_h that way to begin with, but I defined it as a sequence with a recurrence relation similar to A(k), to help draw the analogy between a_1 = 1.08306 and e_1= e/2 = 1.35914. (08/09/2014, 11:10 PM)tommy1729 Wrote: Considering your lastest posts Jay , are you still convinced that J(x)/1.08... is a very good approximation to A(x) ? The reason I wanted to set 1.08306 as a_1 was to make clear what it was. By itself, J(x) is not a perfect approximation of A(k). To Tommy's question, do I consider J(x) a "very good approximation" to A(x)? A "good approximation", yes, but not a "very good approximation". But by re-imagining A(k) as A_1(k), it makes clear why it's not such a good approximation. In reality, it's not so much an issue of J(x) being a poor approximation of A(k). It's that A_1(k) uses such a large step size, that it's a poor approximation of J(x). In this sense, J(x) is the right function to approximate A_1(k), but not the right function to approximate A(k). The distinction is not mathematical, but metaphysical. ~ Jay Daniel Fox « Next Oldest | Next Newest »

 Messages In This Thread My favorite integer sequence - by tommy1729 - 07/27/2014, 08:44 PM RE: My favorite integer sequence - by jaydfox - 07/31/2014, 01:51 AM RE: My favorite integer sequence - by jaydfox - 08/01/2014, 01:53 AM RE: My favorite integer sequence - by Gottfried - 08/01/2014, 03:25 PM RE: My favorite integer sequence - by jaydfox - 08/01/2014, 05:04 PM RE: My favorite integer sequence - by sheldonison - 08/01/2014, 11:36 PM RE: My favorite integer sequence - by jaydfox - 08/01/2014, 11:57 PM RE: My favorite integer sequence - by jaydfox - 08/05/2014, 04:49 PM RE: My favorite integer sequence - by jaydfox - 08/05/2014, 05:57 PM RE: My favorite integer sequence - by Gottfried - 08/06/2014, 04:38 PM RE: My favorite integer sequence - by jaydfox - 08/07/2014, 01:19 AM RE: My favorite integer sequence - by jaydfox - 08/07/2014, 01:34 AM RE: My favorite integer sequence - by jaydfox - 08/09/2014, 09:42 AM RE: My favorite integer sequence - by Gottfried - 08/09/2014, 02:27 PM RE: My favorite integer sequence - by tommy1729 - 09/09/2014, 12:55 AM RE: My favorite integer sequence - by jaydfox - 08/08/2014, 12:55 AM RE: My favorite integer sequence - by Gottfried - 08/08/2014, 02:27 AM RE: My favorite integer sequence - by jaydfox - 09/09/2014, 07:43 PM RE: My favorite integer sequence - by jaydfox - 09/09/2014, 09:45 PM RE: My favorite integer sequence - by jaydfox - 08/02/2014, 12:08 AM RE: My favorite integer sequence - by tommy1729 - 08/03/2014, 11:38 PM RE: My favorite integer sequence - by sheldonison - 08/04/2014, 11:49 PM RE: My favorite integer sequence - by jaydfox - 09/16/2014, 05:32 AM RE: My favorite integer sequence - by Gottfried - 09/17/2014, 07:39 PM RE: My favorite integer sequence - by jaydfox - 10/02/2014, 10:53 PM RE: My favorite integer sequence - by Gottfried - 08/03/2014, 03:32 PM RE: My favorite integer sequence - by tommy1729 - 08/03/2014, 11:44 PM RE: My favorite integer sequence - by sheldonison - 08/02/2014, 05:48 AM RE: My favorite integer sequence - by tommy1729 - 09/10/2014, 08:57 PM RE: My favorite integer sequence - by Gottfried - 08/02/2014, 07:43 PM RE: My favorite integer sequence - by Gottfried - 08/02/2014, 09:29 PM RE: My favorite integer sequence - by Gottfried - 08/02/2014, 09:36 PM RE: My favorite integer sequence - by tommy1729 - 08/05/2014, 11:16 PM RE: My favorite integer sequence - by tommy1729 - 08/08/2014, 11:02 PM RE: My favorite integer sequence - by jaydfox - 08/09/2014, 07:02 PM RE: My favorite integer sequence - by jaydfox - 08/09/2014, 10:51 PM RE: My favorite integer sequence - by sheldonison - 08/11/2014, 04:51 PM RE: My favorite integer sequence - by jaydfox - 08/11/2014, 05:19 PM RE: My favorite integer sequence - by jaydfox - 08/19/2014, 01:36 AM RE: My favorite integer sequence - by jaydfox - 08/19/2014, 02:05 AM RE: My favorite integer sequence - by jaydfox - 08/19/2014, 05:31 PM RE: My favorite integer sequence - by sheldonison - 08/19/2014, 07:56 PM RE: My favorite integer sequence - by jaydfox - 08/20/2014, 07:42 AM RE: My favorite integer sequence - by sheldonison - 08/20/2014, 02:11 PM RE: My favorite integer sequence - by jaydfox - 08/20/2014, 07:57 PM RE: My favorite integer sequence - by jaydfox - 08/21/2014, 01:15 AM RE: My favorite integer sequence - by jaydfox - 08/21/2014, 05:25 AM RE: My favorite integer sequence - by jaydfox - 08/22/2014, 05:39 PM RE: My favorite integer sequence - by jaydfox - 09/11/2014, 01:33 AM RE: My favorite integer sequence - by tommy1729 - 08/09/2014, 09:16 PM RE: My favorite integer sequence - by jaydfox - 08/09/2014, 10:19 PM RE: My favorite integer sequence - by tommy1729 - 08/09/2014, 10:52 PM RE: My favorite integer sequence - by jaydfox - 08/09/2014, 11:46 PM RE: My favorite integer sequence - by tommy1729 - 08/09/2014, 11:10 PM RE: My favorite integer sequence - by jaydfox - 08/10/2014, 12:30 AM RE: My favorite integer sequence - by tommy1729 - 08/11/2014, 12:17 PM RE: My favorite integer sequence - by Gottfried - 08/22/2014, 12:30 AM Amazing variant - by tommy1729 - 08/26/2014, 08:57 PM RE: My favorite integer sequence - by tommy1729 - 09/01/2014, 10:37 PM RE: My favorite integer sequence - by tommy1729 - 10/02/2014, 11:24 PM RE: My favorite integer sequence - by jaydfox - 10/02/2014, 11:29 PM RE: My favorite integer sequence - by tommy1729 - 02/10/2015, 12:15 AM RE: My favorite integer sequence - by tommy1729 - 02/15/2015, 05:19 PM RE: My favorite integer sequence - by tommy1729 - 10/07/2015, 08:22 AM RE: My favorite integer sequence - by tommy1729 - 10/07/2015, 09:10 PM RE: My favorite integer sequence - by tommy1729 - 03/13/2016, 12:31 AM

 Possibly Related Threads... Thread Author Replies Views Last Post My favorite theorem tommy1729 0 4,154 08/15/2015, 09:58 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)