11/06/2007, 07:17 AM
GFR Wrote:How did you know that I was going to post a reply, ... to-day ?!
Hi Gianfranco -
as a double sagittarius sometimes you hit the point without knowing it; and as a practionizer of Zen ... one learns, that the goal attracts the arrow if you simply let it happen... :-)
Well - good that happened. I've read your article: nice coincidence of ideas. Thanks!
I think, it has even the characteristic of a paradigm-change to move from the view as "appending exponents" to the view of "appending bases" - this seems to be much more important than the difficulties of introducing another notation. The question is: how do we embed our view and handling of tetration in the case of infinite height in the very basic and important concept of approximation via partial evaluation (partial sums). In the context of divergent summation, for instance, this seems the main and indispensable prerequisite of all statements about "the value" of an infinite divergent series.
In the understanding of "appending exponents" there is no differing top-exponent in the infinite case, and we have only one fixpoint.
In the understanding of "appending bases" we can deal with all fixpoint, constituting a more complete framework.
I think this is in fact a (however sophisiticated but not superfluous) question of definition of the operation.
Gottfried
Gottfried Helms, Kassel