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 Generalized Kneser superfunction trick (the iterated limit definition) JmsNxn Long Time Fellow Posts: 568 Threads: 95 Joined: Dec 2010 01/25/2021, 01:19 AM (This post was last modified: 01/25/2021, 01:19 AM by JmsNxn.) (01/24/2021, 09:04 PM)MphLee Wrote: ps: why do you use the bullet as composition (instead of \circ)? I use a bullet because I think of it as a product. And it's not exactly the same thing as $\circ$. The bullet acts as a binding variable; so we bound the variable $z$ to $\Omega$. Then, once we've binded it; we can perform group operations (key word group; composition (as said with $\circ$) is not necessarily a group). If I were to write; $ \int_b^c f(s,z)\,ds\circ \int_a^b f(s,z) ds\circ z = \int_a^c f(s,z)\,ds\circ z\\$ It's not entirely obvious that we are, first of all binding $z$ to the integral; and second of all that we are in a group structure. The bullet looks more like multiplication; and its a novel symbol in this scenario; so we don't run into a problem with overriding a symbol that we already use a lot. It's largely an issue with novelty and precision. And trying to hammer home that it means something different than composition; it's composition restricted to a group structure. « 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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