07/03/2017, 07:47 PM

In my view, the composition and iteration are in very friendly relationship... why? Because

Let O be an iteratable operator, let y be a constant and x be a variable. Thus

y O y O ... O y = (y O x)^o(x-1) o N = y O^It x

If O is addition, O^It is multiplication and so on.

But what is N? Well, N is the so-called Neutral number for the operator O, which can be 0 for addition, 1 for multiplication and its iterateds, x for composition, 1 for functional power and its iterateds etc...

So it can be a formula for iteration, but how to repeat ("iterate")? It is iterated iteration... or the correct expression: repeated iteration.

I am interested in this equation:

( (y O x)^o(x-1) o N )^z = y O^(Iterated z times) x

How can we use it? And am I right with these expressions?

Let O be an iteratable operator, let y be a constant and x be a variable. Thus

y O y O ... O y = (y O x)^o(x-1) o N = y O^It x

If O is addition, O^It is multiplication and so on.

But what is N? Well, N is the so-called Neutral number for the operator O, which can be 0 for addition, 1 for multiplication and its iterateds, x for composition, 1 for functional power and its iterateds etc...

So it can be a formula for iteration, but how to repeat ("iterate")? It is iterated iteration... or the correct expression: repeated iteration.

I am interested in this equation:

( (y O x)^o(x-1) o N )^z = y O^(Iterated z times) x

How can we use it? And am I right with these expressions?

Xorter Unizo