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 The fermat superfunction tommy1729 Ultimate Fellow Posts: 1,372 Threads: 336 Joined: Feb 2009 03/23/2014, 12:15 AM (This post was last modified: 03/25/2014, 12:27 AM by tommy1729.) f(x) = x has 2 solutions : 1 and 2. The superfunction F(x) is entire and has the fixpoint (of f(x)) 1 @ complex infinity. Also the other fixpoint 2 occurs for F(x) at - oo. so everything seems to work out nicely. But it might be deception ! F(x) = 2 <=> 2^(2^x) +1 = 2 <=> 2^(2^x) = 1 This has MANY solutions. And that fact seems to make life hard. We cannot blame singularities now since F(x) is ENTIRE ! Does this imply that F(x) is pseudoperiodic or something ? Or does the functional equation fail ? Both seem to weird to be true. Now f(x) has 2 fixpoints. So maybe we need 2 superfunctions ? One seems entire , but to what fixpoint does it belong ? How does the other superfunction behave ? What about those methods where we use 2 fixpoints such as the analytic sickel between two fixpoints based on fatou ? This seems to be as puzzling as tetration itself , hence like I said this is imho " deception ". It is more complicated then it looks. Seems having the entire property does not solve all issues ! Keep in mind that an answer like " oh thats just because of the log branches " is not a " real " answer. I was aware of this for a long time but I was waiting for a response to my first post. Since it did not come I felt the need to explain more. Maybe you agree on the opinion that this is a serious important topic now. regards tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread The fermat superfunction - by tommy1729 - 08/13/2013, 12:23 PM RE: The fermat superfunction - by tommy1729 - 03/23/2014, 12:15 AM RE: The fermat superfunction - by mike3 - 03/23/2014, 11:29 PM RE: The fermat superfunction - by tommy1729 - 03/24/2014, 12:58 AM

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