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Functional super-iteration and hierarchy of functional hyper-iterations
(05/04/2009, 08:04 PM)Tetratophile Wrote: Your operator was defined with my operator. Here is the definition that you gave:

I gave a recursive definition, your operator is defined with my and my is defined with yours. They are defined simulataneously by the equations

(1) .
(3) and

Quote:Your I operator is basically the same as my It operator; the only differnce is the notation. Can you tell me exactly what is different about your definition of the hyper-
iteration rthan mine?

The difference is the declaration: Your operator It_n takes two functions and returns a function. My operator I_n takes a function and a number and returns a function.

Quote:[f It_n g](x) := [f It_n g(x)](x) - Let me clarify what it means.
Its absolutely clear what it means, however you see you make here the implicit distinction between It_n with a function as second argument (left side) and It_n with a number as second argument (right side).
To make the difference explicit rename It_n at the right side to I_n (and change the arrangement slightly). Then this exactly (1).

This equation can not be guessed! It needs to be written as part of the recursive definition!

Messages In This Thread
RE: Functional super-iteration and hierarchy of functional composition-based operations - by bo198214 - 05/04/2009, 08:50 PM

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