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 Generalized Kneser superfunction trick (the iterated limit definition) JmsNxn Long Time Fellow Posts: 551 Threads: 93 Joined: Dec 2010 01/28/2021, 03:50 AM (This post was last modified: 01/28/2021, 03:58 AM by JmsNxn.) I read your paper again, and I think I have some more thoughts, but I have more questions. I think I'll formulate a couple of questions and try to explain myself through an air of questioning; and hone the questions better and then ask. First, I thought it warranted to try to talk categorically. Can we write, $ \mathcal{F} = \{f \in \mathcal{C}(\mathbb{R}^+,\mathbb{R}^+),\,f\,\text{is an isomorphism},\,f' \neq 0\}$ So that $f$ is say, a diffeomorphism (I believe that's the word, if not; it's something like that) of $\mathbb{R}^+$. Just so my shallow brain can think of a representative of the category; and it's not all up in the air. Let's additionally assume that: $ |f(x)| \le Ae^{Bx}$ For some constants $A,B$. Which will make the exponential convergents behave well. And it would imply it's inverse at worse grows like $\log$ somethin' somethin'. This would be a perfectly good algebraic space where we could derive, $ \forall f,g \in \mathcal{F} \exists \phi \in \mathcal{F} f\phi=\phi g$ Now I haven't proven that, not entirely sure how to, but it's manageable--I could probably prove something close enough to continue the discussion. ------------------------- With that out of the way, I'm going to keep thinking about this as operations on $\mathcal{F}$ and functors; but to me they make sense as functors on $\mathcal{F}$; or subgroups, or different versions or whatever. What I mean is, can we think of $\mathcal{F}$ as an almost IDEAL space. Like the best space possible; where all the algebra is simple. Rather than monsters like $e^x$ we look at simple amoebas like $x^2 + x$. And build from the bottom up. Because I agree with a lot of what you are saying. But from a categorical perspective, start simple, no? Unless I'm missing something drastic. You're paper was the most riveting the 3rd time... Maybe I just got over analytical, lmao « Next Oldest | Next Newest »

 Messages In This Thread Generalized Kneser superfunction trick (the iterated limit definition) - by MphLee - 01/22/2021, 03:08 PM RE: Generalizied superfunction trick (the iterated limit definiton) - by JmsNxn - 01/22/2021, 10:10 PM RE: Generalized Kneser superfunction trick (the iterated limit definiton) - by MphLee - 01/24/2021, 09:04 PM RE: Generalized Kneser superfunction trick (the iterated limit definiton) - by JmsNxn - 01/25/2021, 01:19 AM RE: Generalized Kneser superfunction trick (the iterated limit definiton) - by MphLee - 01/25/2021, 11:26 AM RE: Generalized Kneser superfunction trick (the iterated limit definiton) - by JmsNxn - 01/26/2021, 01:05 AM RE: Generalized Kneser superfunction trick (the iterated limit definiton) - by JmsNxn - 01/28/2021, 03:50 AM RE: Generalized Kneser superfunction trick (the iterated limit definiton) - by MphLee - 01/29/2021, 12:02 AM RE: Generalized Kneser superfunction trick (the iterated limit definition) - by MphLee - 02/05/2021, 03:26 PM RE: Generalized Kneser superfunction trick (the iterated limit definition) - by JmsNxn - 02/06/2021, 12:45 AM RE: Generalized Kneser superfunction trick (the iterated limit definition) - by MphLee - 02/27/2021, 11:14 AM RE: Generalized Kneser superfunction trick (the iterated limit definition) - by MphLee - 03/19/2021, 11:10 PM RE: Generalized Kneser superfunction trick (the iterated limit definition) - by JmsNxn - 03/20/2021, 07:18 PM RE: Generalized Kneser superfunction trick (the iterated limit definition) - by JmsNxn - 03/20/2021, 09:55 PM RE: Generalized Kneser superfunction trick (the iterated limit definition) - by MphLee - 03/21/2021, 01:56 AM RE: Generalized Kneser superfunction trick (the iterated limit definition) - by JmsNxn - 03/21/2021, 07:31 AM RE: Generalized Kneser superfunction trick (the iterated limit definition) - by MphLee - 03/21/2021, 12:22 PM RE: Generalized Kneser superfunction trick (the iterated limit definition) - by JmsNxn - 03/22/2021, 08:45 PM RE: Generalized Kneser superfunction trick (the iterated limit definition) - by MphLee - 03/22/2021, 11:01 PM RE: Generalized Kneser superfunction trick (the iterated limit definition) - by JmsNxn - 03/22/2021, 11:30 PM RE: Generalized Kneser superfunction trick (the iterated limit definition) - by JmsNxn - 03/24/2021, 10:20 PM RE: Generalized Kneser superfunction trick (the iterated limit definition) - by JmsNxn - 03/29/2021, 02:54 AM RE: Generalized Kneser superfunction trick (the iterated limit definition) - by MphLee - 05/26/2021, 12:56 AM RE: Generalized Kneser superfunction trick (the iterated limit definition) - by MphLee - 05/26/2021, 10:31 AM RE: Generalized Kneser superfunction trick (the iterated limit definition) - by JmsNxn - 05/26/2021, 11:36 PM RE: Generalized Kneser superfunction trick (the iterated limit definition) - by MphLee - 05/26/2021, 11:55 PM

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