User blog comment:Mh314159/new YIP notation/@comment-39585023-20190714235606/@comment-35470197-20190720223020

I see. Right, we do not have to go beyond higher ordinals. Actually, I am the one who is really interested in any well-defined natural numbers, and any attractive system genaring new natural numbers. I also like to generate a large number under several restrictions, e.g. rules admitting only elementary functions, only 1-ary functions, only inline-functions, and so on. Many of us have preference rather than the pure bigness based on pure mathematics. We can enjoy natural numbers even if they are not the highest among the community.