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Functional super-iteration and hierarchy of functional hyper-iterations
#10
EDIT 5/2/09: For the hierarchy of iterations, or hyper-iterations, we can use the operator:
where It_0 is function composition (g It_0 f = g(f)). All of the operators has the property So unless otherwise specified by the use of the down arrow like this, super-iteration, like other hyper-iterations, is evaluated from the top down, like ordinary tetration, not from the bottom up as I said originally. I am sorry for any confusion the mistake in the original post may have caused.

ANOTHER EDIT 5/2/09: Ictually I am not even sure whether iteration is not associative, but i'll assume it is not unless proven otherwise.
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RE: Functional super-iteration and hierarchy of functional composition-based operations - by Base-Acid Tetration - 05/03/2009, 01:08 PM

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