User blog comment:Mh314159/new YIP notation/@comment-39585023-20190714235606/@comment-39585023-20190718171440

The value of any bracketed expression is defined by line 2, for which the n value is defined by lines 3 and 4. The value of n is a function of the expression you are recursing and therefore will change many times as you recurse a given starting expression. I can change line 4 so that it says something like if a = 1, n = [[b,...,a,ß],b,...,a,ß-1]

"Since the same expression, e.g. 0 0(x), can mean distinct values in your rules, it is impossible for us to determine whether the expressions in the right hand sides take values depending on parameters in line 2. "

Since 0 0(x) is a function that generates a bracketed string, then its value clearly depends on n, since all bracketed values are defined as g n<\sub>n(n) where n is a function of the bracketed string itself, as defined by lines 3 and 4. When the string changes, the value of n used to define its value changes.

This all makes perfect sense to me, but I guess it's not acceptable in the formal rules of math.

So if evaluating [2,2], for example, first we need to know n, which by line 3 = [1,2]. So to know the n for [2,2] we need to know the value of [1,2] which means knowing the n for [1,2], which by line 4 = [[2],1] etc. and of course, each time a recursion reaches 0 0(x) a new bracketed string is generated with a smaller value of beta and its own unique value of n. Should I be expressing n as a function, so that n([2,2]) = [1,2}? And therefore [2,2] = gn([2,2])n([2,2])(n([2,2]))  Does this help clear up the relationship between a bracketed string and the value of n?