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 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

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