• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Ackermann function and hyper operations andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 08/23/2009, 01:37 AM I wanted to say something about the first part, "1 Introduction". In this part of the paper, you equate the original Ackermann function with a[n]b, which (stictly speaking) is not true. Robert Munafo has discussed this on his website (http://www.mrob.com/pub/math/largenum.html), and I have also verified this for myself by reading the original paper Ackermann wrote. Ackermann's tetration is a function $f(n, m) = \phi(n, m, 3) = {}^{(m+1)}n$ which is an offset from tetration. Because it is an offset of tetration, $\phi(n, m, 4)$ is not pentation at all. It wasn't until Reuben Goodstein that the "offset" disappeared. I think we should take this into account when discussing the original Ackermann function, because its evolution is way more complicated than any introduction can really summarize. « Next Oldest | Next Newest »

 Messages In This Thread Ackermann function and hyper operations - by andydude - 08/23/2009, 01:37 AM The Ackermann function - by bo198214 - 08/23/2009, 09:45 AM RE: The Ackermann function - by andydude - 08/24/2009, 01:09 AM RE: The Ackermann function - by bo198214 - 04/18/2011, 05:08 PM

 Possibly Related Threads... Thread Author Replies Views Last Post Thoughts on hyper-operations of rational but non-integer orders? VSO 2 149 09/09/2019, 10:38 PM Last Post: tommy1729 Could there be an "arctic geometry" by raising the rank of all operations? Syzithryx 2 308 07/24/2019, 05:59 PM Last Post: Syzithryx Is there a function space for tetration? Chenjesu 0 192 06/23/2019, 08:24 PM Last Post: Chenjesu Degamma function Xorter 0 669 10/22/2018, 11:29 AM Last Post: Xorter Hyper-volume by integration Xorter 0 1,221 04/08/2017, 01:52 PM Last Post: Xorter Hyper operators in computability theory JmsNxn 5 3,445 02/15/2017, 10:07 PM Last Post: MphLee Recursive formula generating bounded hyper-operators JmsNxn 0 1,332 01/17/2017, 05:10 AM Last Post: JmsNxn holomorphic binary operators over naturals; generalized hyper operators JmsNxn 15 15,295 08/22/2016, 12:19 AM Last Post: JmsNxn Should tetration be a multivalued function? marraco 17 14,917 01/14/2016, 04:24 AM Last Post: marraco Introducing new special function : Lambert_t(z,r) tommy1729 2 3,237 01/10/2016, 06:14 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)