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Infinite tetration and superroot of infinitesimal
#47
Ivars Wrote:But is not applying of infinite log(log(log( .........h(z)) from the right leading back to z?

No, no, no! What h represents is a fixed point of an exponential function. So if then and if you are taking the base-z logarithm of both sides then you can see that which means that a is not only a fixed point of the base-z exponential function, but it is also a fixed point of the base-z logarithm function as well. And if it is a fixed point of the logarithm function, then there is no amount of iteration that will give any other output, so , so infinitely iterated logarithms are not the inverse of infinitely iterated exponentials, only is the inverse of infinitely iterated exponentials.

Andrew Robbins
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RE: Infinite tetration and superroot of infinitesimal - by andydude - 01/08/2008, 11:44 PM

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