01/22/2008, 09:56 PM

andydude Wrote:What you are talking about only applies to binary operations. Integer iteration of one-variable functions is always unique, no matter what. However, when discussing binary operations (which are two-variable functions), there is more than one way to construct a one-variable function from a two-variable function.

Andrew Robbins

Well I will have to read it many times, most likely You have once again made a good explanation - which includes much more I could have imagined when asking the question.

Sometimes I feel that with pentation etc we are making the same circle on a plane above some area, just 1 km higher. Just as scales are relative ( if they are) You have the option to describe all scales by an algorithm (somehow manipulating infinties and infinitesimals logically consistently) or describe all scales in all their complexity - and then You and up with infinite expansion of names, branches , notations etc. Just intuitively, despite Godel's theorem , I can not see math as not beiing possible to close logically while allowing it to develop because of undetermined symbols like infinity, etc..