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A more consistent definition of tetration of tetration for rational exponents
#21
describes the function your assumption produces, i.e.:




and so on, while still allowing and retaining the property .

By the term orbit I'm refering to a term from dynamical systems where, given a point x, the sequence {x, f(x), f(f(x)), ...} is referred to as the orbit of f from x which is a way of referring to iteration without referring to the t in . By using it this way, though, I'm slightly misusing it, since its a sequence, and not a function. Here I'm using it as a function , sorry if it was confusing. One of the reasons why I like the term 'orbit' so much is that it pairs nicely with iterate which, given t, is a function . I've discussed these terms here as well.

Andrew Robbins
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RE: A more consistent definition of tetration of tetration for rational exponents - by andydude - 10/21/2007, 07:19 AM

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