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 Should tetration be a multivalued function? marraco Fellow Posts: 99 Threads: 12 Joined: Apr 2011 01/04/2016, 12:08 AM (This post was last modified: 01/04/2016, 12:17 AM by marraco.) (01/04/2016, 12:01 AM)andydude Wrote: It appears that these 3 branches are not connected in the real line, but I would suspect that they are connected in the complex plane (to make a Riemann surface), and that fixing ${}^0a = 1$ on the main branch might fix the value of the other branches, at least that's what I would think.[Note: the asymptotes make 5 branches] If the transition is not singular, then the blue branch should be coincident with the black (main) branch for $\vspace{15}{a>e^{e^{-1}}}$. That may give a clue about his better value for °a. [Edit: the transition for the blue branch must be singular, because it cannot smoothly change from an horizontal asymptote to a parallel line to the main branch, which has a vertical asymptote. That unless tetration introduces a new kind of numbers which are continuous in the transition.] They should be coincident, because for the blue branch, any value chosen for °a, is also somewhere in the main branch, so taking iterated logarithms/exponentiations should give the same result. I have the result, but I do not yet know how to get it. « Next Oldest | Next Newest »

 Messages In This Thread Should tetration be a multivalued function? - by marraco - 01/03/2016, 11:24 PM RE: Should tetration be a multivalued function? - by marraco - 01/03/2016, 11:32 PM RE: Should tetration be a multivalued function? - by andydude - 01/03/2016, 11:55 PM RE: Should tetration be a multivalued function? - by andydude - 01/04/2016, 12:01 AM RE: Should tetration be a multivalued function? - by marraco - 01/04/2016, 12:08 AM RE: Should tetration be a multivalued function? - by andydude - 01/04/2016, 12:35 AM RE: Should tetration be a multivalued function? - by marraco - 01/04/2016, 03:57 AM RE: Should tetration be a multivalued function? - by marraco - 01/08/2016, 06:26 PM RE: Should tetration be a multivalued function? - by marraco - 01/08/2016, 11:05 PM RE: Should tetration be a multivalued function? - by sheldonison - 01/09/2016, 06:20 AM RE: Should tetration be a multivalued function? - by marraco - 01/09/2016, 05:56 PM RE: Should tetration be a multivalued function? - by marraco - 01/14/2016, 04:24 AM RE: Should tetration be a multivalued function? - by tommy1729 - 01/10/2016, 03:37 AM RE: Should tetration be a multivalued function? - by marraco - 01/11/2016, 09:28 PM RE: Should tetration be a multivalued function? - by andydude - 01/13/2016, 08:24 AM RE: Should tetration be a multivalued function? - by sheldonison - 01/13/2016, 01:37 PM

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