andydude Wrote:Also, GFR uses x$y*a or something like that, which I find confusing.

Hey Andrew! I think that we have a misunderstanding here. Your citation, without ... warnings is also misleading. As a matter of fact, we adopted a special notation, at rank 4, for the representation of large numbers, based on an expression of a number z, such as:

z = b^(b^(b^ ...(b^x)...)), where b^ was supposed to be iterated n times (h?). This gives, for instance (n=3, x<b):

z = b^(b^(b^x)) = x @ (b#3) = b # (3+q), with q = slog_b x.

[in fact: 3+q = slog_b z, then: q = slog_b z -3 = slog_b x].

@ stands here for the "last" exponent appended to the tower height, corresponding to "mantissa" q (q<1). It is only a notation of numbers similar to the floating point scientific notation (always x<b):

z = b*b*b*x = x* (b^3) = b ^ (3+q), with q = log_b x.

So, indeed, I could write:

z = x @ (b#n)

for a "tower" with base b, height n and "tower extension" x. It's not confusing, in this particular application. In case of "integer" h iterations (..!) of a variable x, we could perhaps also write:

z = x @ (b#h) [x "appended" at the "top" of b#h]

But this was not a general notation proposal. It was an ad-hoc tetrational notation for the special purpose that I just mentioned.

And, of course, I agree that h = slog_b z - slog_b x, i.e.:

h = b[4]\ z - b[4]\ x

GFR