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 Pentation's definitional ambiguity Base-Acid Tetration Fellow Posts: 94 Threads: 15 Joined: Apr 2009 10/17/2009, 09:54 PM (This post was last modified: 10/18/2009, 02:51 AM by Base-Acid Tetration.) An important moral question is facing us, my fellow friends of hyper-operations. As we all know, tetration, having log^n singularites for all n, has an infinite number of branches. When we define pentation as a tetration-iterational (superfunction of tetration), we face ambiguity of definition: WHICH branch of tetration SHOULD we mean? Restricting tet(z) to its principal branch (defined for the complex plane excluding (-infinity, -2]) seems the most "correct" definition, but at the same time the most unnatural. The same problem goes for hexation since the superlogarithm has two conjugate branch points, penta-logarithm will have a penta-logarithmic singularity at fixed point of tetration. (It is not known whether pentation has any complex fixed points.) This is a highly subjective question that won't be settled by any amount of attempted rigor, so I propose a split up classification of pentations that we will study. I think we should define "proper pentation" as the function that has pen(z+1)= Tet(pen(z)), where Tet = mainly prinicipal branch of tetration. Or can't we study properties that will apply for all pentations? « Next Oldest | Next Newest »

 Messages In This Thread Pentation's definitional ambiguity - by Base-Acid Tetration - 10/17/2009, 09:54 PM RE: Pentation's definitional ambiguity - by andydude - 10/22/2009, 07:54 AM RE: Pentation's definitional ambiguity - by Base-Acid Tetration - 10/22/2009, 11:40 AM RE: Pentation's definitional ambiguity - by andydude - 10/22/2009, 08:27 PM RE: Pentation's definitional ambiguity - by Base-Acid Tetration - 10/22/2009, 09:45 PM Number of branches of tetration - by bo198214 - 10/24/2009, 09:27 AM RE: Number of branches of tetration - by Base-Acid Tetration - 10/24/2009, 01:02 PM RE: Number of branches of tetration - by bo198214 - 10/24/2009, 01:20 PM RE: Number of branches of tetration - by Base-Acid Tetration - 10/24/2009, 01:23 PM RE: Number of branches of tetration - by bo198214 - 10/24/2009, 02:01 PM RE: Pentation's definitional ambiguity - by Base-Acid Tetration - 12/15/2009, 08:52 PM RE: Pentation's definitional ambiguity - by bo198214 - 12/15/2009, 10:56 PM RE: Pentation's definitional ambiguity - by Base-Acid Tetration - 12/15/2009, 11:08 PM RE: Pentation's definitional ambiguity - by bo198214 - 12/15/2009, 11:15 PM RE: Pentation's definitional ambiguity - by Base-Acid Tetration - 12/15/2009, 11:23 PM

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