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?
(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