User blog comment:DrCeasium/Hyperfactorial array notation: Analysis part 2/@comment-5529393-20130527105642/@comment-5529393-20130528012734

Hmm, so [2,1...,1,2]w/[1] does not mean the array has n entries before the final 2? I thought that w/ was just a shorthand for your already defined notation, but now it looks like it is an extension to your notation. You need to define exactly what it means in all cases, then - for example, what does a chain of w/ mean?

We can still examine [1 (1) 2], which wasn't defined using w/. Your rules on your webpage are unclear, since technically [1 (1) 2] does not meet the requirements of either R1 or R2; it is not either [@1(a)1(b)m(c)@] or [@1(a)y,@21,m,@]. Clearly there are many arrays that do not fit these descriptions;  you should clarify if @1(a) and @ could be empty, whether y and m are required to be greater than 1, what happens when the first entry is greater than 1, etc. Don't assume people will understand what you mean; define all cases explicitly!

Anyway, I will assume [1 (1) 2] is intended to be defined using R1, and that n![1 (1) 2] = n![Z_n], where Z_0 = n and Z_{i+1} = n![n, n, ..., n] with Z_i n's.  This is exactly what I described before;  an array of length n is approximately \(F_{\phi(\omega)}(n)\), and we apply the function n times, so n![1 (1) 2] is approximately \(F_{\phi(\omega)+1}(n)\), not \(F_{\Gamma_0}(n)\)