User blog comment:Scorcher007/S - Large Countable Ordinal Notation. Chapter I, Up to KPm./@comment-35470197-20190912034735

> where x - axiom of existence admissible ordinal or limit of admissible in this well-formed notation

> x - axiom of large countable ordinal

I could not understand the precise meaning. Are you assuming the existence of the ordinal itself instead of the usual axioms on the universe? Is there a known relation between your axioms and the usual axioms?

> How to get finite numbers:

If you are intending the functions in this section are strictly increasing, the value of \(\lim_{n \to \omega}\) is infinity. Therefore the inequality is wrong. I guess that you are not intending what you wrote, but the eventual domination.