User blog:Alejandro Magno/FGH Notation

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Basic
f_0,1(n) = f_f_f_..._f_f_n(n)(n)(n)...(n)(n)(n)

f_1,1(n) = f_0,1(f_0,1(...(f_0,1(n))...)) with n levels

f_0,2(n) = a --> f_a,1(n)

f_0,m(n) = a --> f_a.m-1(n)

f_0,0,1(n) = a --> f_0,a(n)

f_0,1,1(n) = a --> f_a,0,1(n)

f_0,0,2(n) = a --> f_0,a,1(n)

etc.

Comparisons
(here values are in fgh (f_@(n)))

0,1 --> w+1

1,1 --> w+2

0,2 --> w*2

0,0,1 --> w^2

0,1,1 --> w^2+w

0,0,2 --> w^2*2

0,0,0,1 --> w^3

etc.

So limit is w^w

Introducing the f
f_f(n) = f_0,0,0,...,0,0,1(n) with n entries

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