Right you are! Nevertheless, I always assumed that tetration was:

- 3-tetra-3 = 3#3 = 3^(3^3) = 3 ^ 27 = 7.62559747... x 10^12; and not:

- (3^3)^3 = 3^(3x3) = 3^(3^2) = 3^9 = 19683 [a ... collapsing tower].

This above-mentioned assumption, in my opinion, is to be considered valid for all the hyper-operation hierarchy, because it defines an "elementary" operation. For level 4, in my opinion, right priority towers are the correct definition of tetration. "Left priority towers" ("left tetrates") are not elementary operations. In fact:

- ((a^a)..^a)^a) [n times] = a^(a^(n-1) [un-homogeneous collapsed tower]

But, of course you are right. We must adopt a convention (that one, ... in my opinion), otherwise it would be impossible to talk of y = e # x = e-tetra-x = sexp x and/or of the superlog.

Other various bracketing conventions, like a^(a^(a^a))^a can be dealt with by the fully flexible Reihenalgebra (see Henryk's methodology).

GFR

- 3-tetra-3 = 3#3 = 3^(3^3) = 3 ^ 27 = 7.62559747... x 10^12; and not:

- (3^3)^3 = 3^(3x3) = 3^(3^2) = 3^9 = 19683 [a ... collapsing tower].

This above-mentioned assumption, in my opinion, is to be considered valid for all the hyper-operation hierarchy, because it defines an "elementary" operation. For level 4, in my opinion, right priority towers are the correct definition of tetration. "Left priority towers" ("left tetrates") are not elementary operations. In fact:

- ((a^a)..^a)^a) [n times] = a^(a^(n-1) [un-homogeneous collapsed tower]

But, of course you are right. We must adopt a convention (that one, ... in my opinion), otherwise it would be impossible to talk of y = e # x = e-tetra-x = sexp x and/or of the superlog.

Other various bracketing conventions, like a^(a^(a^a))^a can be dealt with by the fully flexible Reihenalgebra (see Henryk's methodology).

GFR