User blog comment:Mh314159/A new notation for large numbers/@comment-39585023-20190610200105/@comment-24725252-20190611004105

You are vastly underestimating how large TREE(3) is. You can't beat TREE(3) with meager recursion of numbers. The reason why TREE(3) can be reached with the FGH is because we have to use ordinals up to the SVO, which are insanely complicated for a beginner like you. The FGH's strength comes not from the recursion, but from the structure of ordinals, which create insanely powerful recursion, which your notation doesn't have. So, your notation only reaches slightly past w^3+w+1 in the FGH, while TREE(3) reaches past the SVO.