Hi Henryk!
Coirrect! However, also limiting ourselves to rank 4 (tetration), appropriate writings for the superexp or tower (tetra, sexp or tow, with base b) and its right-inverse, superlog (slog, to the base b) are not sufficient.
We should not forget its left-inverse, superroot (srt, n degree). Think, for instance, of the super-squareroot or square-superroot, solution of equation y = x ^ x, that we can write y = x # 2, with x = ssrt(y). Superlog and superroot are the two inverse operations of the superexp, tetra(tion), or tower, operation. They all belong to the tetration rank (s=4). Other general hyperroots mightl indeed come later.
GFR
Coirrect! However, also limiting ourselves to rank 4 (tetration), appropriate writings for the superexp or tower (tetra, sexp or tow, with base b) and its right-inverse, superlog (slog, to the base b) are not sufficient.
We should not forget its left-inverse, superroot (srt, n degree). Think, for instance, of the super-squareroot or square-superroot, solution of equation y = x ^ x, that we can write y = x # 2, with x = ssrt(y). Superlog and superroot are the two inverse operations of the superexp, tetra(tion), or tower, operation. They all belong to the tetration rank (s=4). Other general hyperroots mightl indeed come later.
GFR