User blog comment:Mh314159/A hopefully powerful new system/@comment-33713741-20190627114835/@comment-35470197-20190627151756

> Since I'm not a mathematician I cannnot relate what I've done to ordinal theory.

There are few mathematicians here. Many googologists here just study ordinals by themselves to create stronger notations.

Well, I do not mind if you do not want to learn ordinals. We can enjoy googology as freely as we wish. Studying recursion is also good.

To begin with, it is better not to use "…". It is intuitive, and often causes errors. For example, when you write [n][a,b,c,...p,q], does it mean the second bracket contains at least six entries? Maybe not, because you write examples with two entries. Definitions should be clearly uniquely readable even if you do not have examples. Then examples help other to understand them deeper. At least, I could not understand why [n][p+1,1] = n][p,1p+1][p,1 in the example holds. According to your definition, you have [n][p+1,1] = n][p,1p+1][p,1],[1][p,1 but not the equality in the example. I guess that your definition is incomplete.