• 1 Vote(s) - 1 Average
• 1
• 2
• 3
• 4
• 5
 Tetration extension for bases between 1 and eta dantheman163 Junior Fellow Posts: 13 Threads: 3 Joined: Oct 2009 11/07/2009, 11:30 PM If we set $f(x+1)=b^{f(x)}$ which is to say $\lim_{k\to \infty} (log_{b}^{ok}((x+1)({}^k b- {}^{(k-1)} b)+{}^k b) ) = \lim_{k\to \infty} (log_{b}^{o(k-1)}(x({}^k b- {}^{(k-1)} b)+{}^k b) )$ then reduce it to $\lim_{k\to \infty} (log_{b}((x+1)({}^k b- {}^{(k-1)} b)+{}^k b) ) = \lim_{k\to \infty} (x({}^k b- {}^{(k-1)} b)+{}^k b)$ Then just strait up plug in infinity for k we get $log_{b} {}^\infty b = {}^\infty b$ which is the same as ${}^\infty b = {}^\infty b$ This is really weird because if i do $\lim_{k\to \infty} (log_{b}^{ok}(1({}^k b- {}^{(k-1)} b)+{}^k b) )$ for $b= sqrt2$ i get about 1.558 which is substantially larger then $sqrt2$ Can anyone else confirm that $\lim_{k\to \infty} (log_{b}^{ok}(1({}^k b- {}^{(k-1)} b)+{}^k b) ) \approx 1.558$ for $b= sqrt2$ ? « Next Oldest | Next Newest »

 Messages In This Thread Tetration extension for bases between 1 and eta - by dantheman163 - 11/05/2009, 03:00 AM RE: Tetration extension for bases between 1 and eta - by bo198214 - 11/05/2009, 01:44 PM RE: Tetration extension for bases between 1 and eta - by dantheman163 - 11/05/2009, 11:53 PM RE: Tetration extension for bases between 1 and eta - by bo198214 - 11/07/2009, 09:31 AM RE: Tetration extension for bases between 1 and eta - by bo198214 - 11/07/2009, 05:11 PM RE: Tetration extension for bases between 1 and eta - by bo198214 - 11/07/2009, 08:12 PM RE: Tetration extension for bases between 1 and eta - by dantheman163 - 11/07/2009, 11:30 PM RE: Tetration extension for bases between 1 and eta - by bo198214 - 11/08/2009, 02:44 PM RE: Tetration extension for bases between 1 and eta - by mike3 - 11/12/2009, 07:11 PM RE: Tetration extension for bases between 1 and eta - by dantheman163 - 12/15/2009, 01:01 AM RE: Tetration extension for bases between 1 and eta - by bo198214 - 12/15/2009, 01:40 AM RE: Tetration extension for bases between 1 and eta - by dantheman163 - 12/15/2009, 01:48 AM RE: Tetration extension for bases between 1 and eta - by dantheman163 - 12/17/2009, 02:40 AM RE: Tetration extension for bases between 1 and eta - by bo198214 - 12/17/2009, 10:59 AM RE: Tetration extension for bases between 1 and eta - by dantheman163 - 12/19/2009, 05:06 AM RE: Tetration extension for bases between 1 and eta - by bo198214 - 12/19/2009, 10:55 AM

 Possibly Related Threads... Thread Author Replies Views Last Post Possible continuous extension of tetration to the reals Dasedes 0 1,500 10/10/2016, 04:57 AM Last Post: Dasedes Andrew Robbins' Tetration Extension bo198214 32 46,487 08/22/2016, 04:19 PM Last Post: Gottfried Why bases 0 2 tommy1729 0 1,986 04/18/2015, 12:24 PM Last Post: tommy1729 on constructing hyper operations for bases > eta JmsNxn 1 3,027 04/08/2015, 09:18 PM Last Post: marraco Non-trivial extension of max(n,1)-1 to the reals and its iteration. MphLee 3 4,193 05/17/2014, 07:10 PM Last Post: MphLee extension of the Ackermann function to operators less than addition JmsNxn 2 4,371 11/06/2011, 08:06 PM Last Post: JmsNxn Alternate solution of tetration for "convergent" bases discovered mike3 12 19,399 09/15/2010, 02:18 AM Last Post: mike3 my accepted bases tommy1729 0 2,362 08/29/2010, 07:38 PM Last Post: tommy1729 [Regular tetration] bases arbitrarily near eta Gottfried 0 2,974 08/22/2010, 09:01 AM Last Post: Gottfried

Users browsing this thread: 1 Guest(s)