User blog comment:Mh314159/Alpha numbers (and beyond)/@comment-35470197-20191007022858/@comment-35470197-20191016094213

I fixed the latex error. Could you read equations in my comment above?

I like to help googologists who are honestly trying to reach their highest levels. Therefore I will read the new rule later. By the way, I recommend you to write new blog posts instead of trying new ideas only in comments. Then other people can find arguments without scrolling many comments. (Personally, comments are not visible from my mobile phone, and hence my analysis will be later.)

Before analysis, it is good to know that using ordinals is not a goal for majority of googologists. Their goal is actually to create a computable large number, which should be given by a numerical notation without ordinals. The reasons why we sometimes talk about ordinals are: Therefore we actually share the goal.
 * 1) It is easy to describe the growth rate.
 * 2) Using ordinals, we can grasp a new idea to create a numerical notation without ordinals. (The main tool is called an ordinal notation, which is not an ordinal but a numerical system.)
 * 3) Unfortunately, several googologists use ordinal without knowing what ordinals are. Namely, they believe that they can directly use ordinals in order to give a computable large number.