User blog:Bubby3/Letter notation extension to Q (e0)

I am going to extend PsiCubed's letter notation up to epsilon-0, with Q, before he makes an offical extension.

Planar arrays
With the definitoin of the array notation and the ltter P, one can easily define palanar array notation function. In this notation, the comma is short for [0], and the dimensional seperator is [1]. Z's represent 0's and dimensional seperators, and k zeroes. k+1 zerores means a group of zeroes and dimensional seperators starting with at least 1 zero. k zeroes is that but it doesn't need to start with a zero Rule 2 and 3 are the case where the last nonzero entry is at the end of a plane and is an iteger. Rule 4 is when the last nonzero entry is at the end of a plane, you use the fractional part of the last entry, and put it in the next row.
 * 1) Other rules are the same from linear array notation
 * (a,b,c...m+1[1]0,z)|x = (a,b,c,...,m[1]1,0,0,z.)|10^(x-1) for 12
 * (a,b,c,...,x[1]0,z)|10 = (a,b,c,...,int(x)[1]10^frac(k),0,...,0,z)|1 with int(k) 0's where k = frac(x)*10
 * 1) (...[1]0,...,0,a,b...)|x = (...[1]a,b...)|x

Higher dimensional arrays
What about fractional number of rows, columns, etc.. In this part, [0] is the comma. z is an array of 0's and dimensional seperators.

Definiton of [a]b:
 * 1) [a+1]b+1 = [a+1]b+1[a]0
 * 2) [a+1]b = [a]10*b for 02
 * (a,b,c,...,x[d+1]0,z)|10 = (a,b,c,...,int(x)[d+1][d]frac(x)*10)|1 with int(k) 0's where k = frac(x)*10
 * (a,b,c,...,n+1[x]0,z)|10 = (a,b,c,...,n[x][int(x)]10^frac(x),z)|10

Letter Q up to R3
aR2 = (1[a]0)|10 and aRb = R(b+log(a)) for a and b < 10. This takes us up to R3 or w^w^w