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Functional super-iteration and hierarchy of functional hyper-iterations
(05/03/2009, 03:25 PM)bo198214 Wrote:
(05/03/2009, 01:08 PM)Tetratophile Wrote: where It_0 is function composition (g It_0 f = g(f)). All of the operators has the property

It is a bit sloppy and misunderstandable to write or in the second argument. As one would associate the function , but actually you mean the constant function:

To make it a definition that makes at least on the natural numbers sense, we need to add the induction start:

The question then however is how do we know what for a non-constant function in the second argument is?

I think to properly define the hierarchy we need an additional operator

such that .


My brain is flickering, I hope I got everything right.

For the function x -> x+1, you simply hyper-n-iterate the function f x0+1 times at x=x0, (eg. at x=2 you iterate 3 times, and at x=3.5 you iterate 4.5 times etc.) So I don't think that a non-constant function in the second argument would behave differently from a constant function in this respect.

Also would not be true, because at n=0, Use of the operator would make the notation more compact, however

Messages In This Thread
RE: Functional super-iteration and hierarchy of functional composition-based operations - by Base-Acid Tetration - 05/03/2009, 07:21 PM

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