02/26/2008, 09:26 AM

Ivars Wrote:r= phi^(1/phi) , r= phi^(1/phi)^phi, r= phi^(1/phi)^phi^(1/phi) etc

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Now we think that infinity^(1/infinity) which was the beginning of this thread is not very well defined.

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So why not define the limits using the finite tangent angles? Or their trigonometric functions, e.g tangens? The one of the outgoing/incoming spiral for infinitesimal^(1/infinitesimal), the one of the limit circle at crossing for infinity^1/infinity.

There are options to define those limits , why no one is used?

I dont understand why you invoke a polar graph here, the limits are very well defined and well-known:

You can already guess it when you look at the (cartesian) graph of the selfroot.

Here we know that for and hence for and hence . Finally again: