09/18/2016, 10:36 AM

Composition: f(x) o c = f( c )

Iterated composition (steinix-ankh): ☉f(x)☥^n_x = f(x)of(x)o...of(x) n times

Iterator-ankh operator: It aOb ☥ = ☉ aOb ☥^n-1_b |(b=a)|(n=b)

It a+b ☥ = ☉ a+b ☥^n-1_b |(b=a)|(n=b) = a+(a+(a+...a+b))|(b=a)|(n=b) = a*b

It a*b ☥ = a^b

It a^b ☥ = a^^b (tetration)

...etc.

It FoG ☥ = ☉ F ☥^G

Now, we know how to iterate operators. But I do not know how to iterate functions, or my question: What is the inverse method of iteration?

Iterated composition (steinix-ankh): ☉f(x)☥^n_x = f(x)of(x)o...of(x) n times

Iterator-ankh operator: It aOb ☥ = ☉ aOb ☥^n-1_b |(b=a)|(n=b)

It a+b ☥ = ☉ a+b ☥^n-1_b |(b=a)|(n=b) = a+(a+(a+...a+b))|(b=a)|(n=b) = a*b

It a*b ☥ = a^b

It a^b ☥ = a^^b (tetration)

...etc.

It FoG ☥ = ☉ F ☥^G

Now, we know how to iterate operators. But I do not know how to iterate functions, or my question: What is the inverse method of iteration?

Xorter Unizo