User blog comment:Ubersketch/A better Fast Growing Hierarchy: The Uber Hierarchy/@comment-30754445-20180922205035/@comment-34422464-20180922222054

You have very very good points. But the purpose of this notation ISN’T to be more powerful than the FGH. It’s made to be more versatile. Where FGH merely approximates functions, this can exactly copy those functions. And same with your point with ordinals encompassing every separator, although ordinals are powerful as every separator, they might not be as versatile as every separator. This notation’s point isn’t to be more powerful than the FGH, it’s supposed to be more versatile.