02/06/2008, 03:01 PM

I think that the infinite (contable) hyper-operation hierarchy y = b[s]x can (... probably!) be extended also to the ranks lower than zero. Nevertheless, please wait for the next thread on zeration. Concerning fractional (... rational) ranks, there is a possibility to define an operation between addition and multiplication (s=0.5 ?) apparently justified by the Gauss' Arithmetic-Geometric mean. We shall talk also of that. All this needs careful analysis and very precise demonstrations.

All non-commutable hyper-operations imply two inverses (the left- and the right- inverse operation), that we can define as belonging to the root and to the log types. This is the case of all integer ranks s >= 3 (exponentiatoion).

For the moment (...), we know that at ranks s=1 (addition) and s= 2 (multiplication), both commutable, these two inverse operations coincide.

GFR

All non-commutable hyper-operations imply two inverses (the left- and the right- inverse operation), that we can define as belonging to the root and to the log types. This is the case of all integer ranks s >= 3 (exponentiatoion).

For the moment (...), we know that at ranks s=1 (addition) and s= 2 (multiplication), both commutable, these two inverse operations coincide.

GFR