Notations and Opinions

[Gottfried]

Please tell me what you (BO, and ... all of you) think of it.
Gianfranco

Dear Gianfranco (and all) -

the proposals are nice.

However, noting, that we find a route for tetrational notation now, I feel I should explicitely re-remark, that for iterated exponentiation and decremented iterated exponantiation, with which I'm involved, I always need three parameters, one additional for the top-(beginning)-exponent x for y= b^..^b^x, height h (= b's in number of h, or more generally: h being the iteration-count) and I should step away a bit and use different symbols.
So I better announce (the ascii-notation)

y = x{4,b}h for iterated exponentiation beginning at x: b^...^b^b^x
(and from earlier discussions)
y = x{3,b}h for iterated multiplication beginning at x: x*b^h
y = x{2,b}h for iterated addition beginning at x: x+b*h

for my needs for the time being,
the "height"-function
h = hgh(x,b)
if
x = 1 {4,b} h
= b [4] h // related to the tetrational notation

just to prevent confusion between these two concepts and the reading of my notes in context of the tetration-discussion.

Gottfried