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Functional super-iteration and hierarchy of functional hyper-iterations
#11
(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 .
with

and

My brain is flickering, I hope I got everything right.
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Messages In This Thread
RE: Functional super-iteration and hierarchy of functional composition-based operations - by bo198214 - 05/03/2009, 03:25 PM

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