• 1 Vote(s) - 2 Average
• 1
• 2
• 3
• 4
• 5
 interesting pattern in hyper-operations BenStandeven Junior Fellow Posts: 27 Threads: 3 Joined: Apr 2009 05/04/2009, 09:15 PM (05/03/2009, 08:20 PM)bo198214 Wrote: (05/02/2009, 08:11 PM)BenStandeven Wrote: (05/01/2009, 01:34 PM)bo198214 Wrote: BenStandeven Wrote:would be approximately true by induction, and we always have e ^k^ 0 = 1, and e ^^ x = x+1 approximately on [-1, 0]. The degree of approximation might decay a bit at each level, I suppose. Hm, you mean there is a function that is closest (say by maximum difference or by area between graphs) to the linear function on the interval [-1,0] among the solutions of f(x+1)=e[k]f(x)? Yeah; I'm thinking that it will probably be e[4] or e[5], since for the higher functions I would expect the deviation from linearity to be greatest on the outer intervals like [-1, 0], and least near the middle. What I rather meant is whether this would be a uniqueness criterion. I.e. whether there is only one function with minimal distance to the linear function [-1,0]? What do you think? I doubt it; I'd think by composing with the right 1-periodic function, you can always move closer to linearity on that interval. « Next Oldest | Next Newest »

 Messages In This Thread interesting pattern in hyper-operations - by Base-Acid Tetration - 04/30/2009, 04:15 AM RE: interesting pattern in hyper-operations - by andydude - 04/30/2009, 05:35 AM RE: interesting pattern in hyper-operations - by andydude - 04/30/2009, 05:53 AM RE: interesting pattern in hyper-operations - by BenStandeven - 04/30/2009, 10:41 PM RE: interesting pattern in hyper-operations - by Base-Acid Tetration - 05/01/2009, 10:22 AM RE: interesting pattern in hyper-operations - by bo198214 - 05/01/2009, 01:34 PM RE: interesting pattern in hyper-operations - by BenStandeven - 05/02/2009, 08:11 PM RE: interesting pattern in hyper-operations - by bo198214 - 05/03/2009, 08:20 PM RE: interesting pattern in hyper-operations - by BenStandeven - 05/04/2009, 09:15 PM

 Possibly Related Threads... Thread Author Replies Views Last Post Interesting commutative hyperoperators ? tommy1729 0 201 02/17/2020, 11:07 PM Last Post: tommy1729 Very interesting topic Ansus 0 595 10/01/2019, 08:14 PM Last Post: Ansus Thoughts on hyper-operations of rational but non-integer orders? VSO 2 927 09/09/2019, 10:38 PM Last Post: tommy1729 Could there be an "arctic geometry" by raising the rank of all operations? Syzithryx 2 1,118 07/24/2019, 05:59 PM Last Post: Syzithryx Hyper-volume by integration Xorter 0 1,599 04/08/2017, 01:52 PM Last Post: Xorter Hyper operators in computability theory JmsNxn 5 4,726 02/15/2017, 10:07 PM Last Post: MphLee Recursive formula generating bounded hyper-operators JmsNxn 0 1,717 01/17/2017, 05:10 AM Last Post: JmsNxn holomorphic binary operators over naturals; generalized hyper operators JmsNxn 15 17,875 08/22/2016, 12:19 AM Last Post: JmsNxn Tetration series for integer exponent. Can you find the pattern? marraco 20 18,615 02/21/2016, 03:27 PM Last Post: marraco Intresting ternary operations ? tommy1729 0 1,769 06/11/2015, 08:18 AM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)