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Functional super-iteration and hierarchy of functional hyper-iterations
#19
(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) .
(2)
(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!
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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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