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 Inverse super-composition Xorter Fellow Posts: 93 Threads: 30 Joined: Aug 2016 11/24/2016, 12:53 PM Let us invastigate the composition and its iterated function. We know the followings: (f o g) o g^-1 = f f^-1 o (f o g) = g ☉ f ☥^N = f o f o ... o f (N times), where ☉ is called steinix and ☥ is called ankh. ☉ f ☥^N o ☉ f ☥^M = ☉ f ☥^(N+M) ☉(☉ f ☥^N)☥^M = ☉ f ☥^(N*M) f o ☉ f ☥^N = ☉ f ☥^N o f = ☉ f ☥^(N+1) ... etc. The question is that what the inverses of the ☉ f(x) ☥^N, steinix-ankh formula is? According to the previous rules, I can find one of the inverses which is the next: ☉(☉ f ☥^N)☥^(1÷N) = f But I am interested in that what the other inverse is which would give me N. So ☉ f ☥^N {something operator}(f) = N, what is it? (It might be called steinix-logarithm.) Any thoughts? Xorter Unizo « Next Oldest | Next Newest »

 Messages In This Thread Inverse super-composition - by Xorter - 11/24/2016, 12:53 PM RE: Inverse super-composition - by JmsNxn - 11/25/2016, 08:55 PM RE: Inverse super-composition - by Xorter - 12/23/2016, 01:33 PM RE: Inverse super-composition - by JmsNxn - 12/23/2016, 08:12 PM RE: Inverse super-composition - by Xorter - 12/24/2016, 09:53 PM RE: Inverse super-composition - by sheldonison - 12/25/2016, 04:16 AM RE: Inverse super-composition - by Xorter - 12/25/2016, 04:38 PM RE: Inverse super-composition - by sheldonison - 12/25/2016, 08:35 PM RE: Inverse super-composition - by Xorter - 12/25/2016, 10:23 PM RE: Inverse super-composition - by sheldonison - 12/26/2016, 07:10 AM RE: Inverse super-composition - by Xorter - 01/12/2017, 04:19 PM RE: Inverse super-composition - by Xorter - 05/26/2018, 12:00 AM

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