User blog comment:Mh314159/new YIP notation/@comment-39585023-20190705220451/@comment-39585023-20190707032451

Thanks. I did notice when I found my nontermination error in my private version of [1] that I should not be using a constant for {m}0(x) = {m-1}mm(x) and will change it to {m}0(x) = {m-1}{m} 0(x-1) (x) and also that the extra function power is not necessary for m of any size because when the subscript decreases by one we will get a large superscript anyway. And I was using m as a constant and then also recursing it, so I'm now using p to stand for the constant [a-1] and m is a variable. Here's the new definition of [a] and at least when I work out [1] it is much, much larger than before. And I have not yet make the similar changes to m is a variable for the [a,b] and beyond definitions.

Single bracketed number:

[0] = 1

p = [a-1]

[a] = {p}p(a)

{m}y(x) = {m}y-1{m}y(x-1)(x)

{m}y(1) = {m}y-1(y+1)

{m}0(x) = {m-1}{m} 0(x-1) (x)

{0}0(x) = fx(x)