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

First of all, thank you to everyone who looked at this and especially those who took the time to comment. This recursion was the result of a personal challenge I set myself relating to a game I played with my students. Can I devise an exact computable algorith that generates a number greater than TREE(3)? I'd like to respectfully ask if those who looked at my recursion and answered not were looking closely enough. I looked at the FGH, and first I'd like to point out that if written in functional notation, the single bar function a|b is the same as fa+1(b) = fafa(b-1)(b) which I is closely related to the fast-growing hierarchy, faster in fact, except perhaps for the smallest values of a and b. Am I mistaken? If I am not mistaken, then perhaps it is significant that 2|4 is in the Conway chain range, and therefore already at the “lower case omega” level of recursion in the FGH? It is hard for me to find a frame of reference for numbers like 2|5. And 3|3, for example, is much much larger. And then if we look at 1||2 which is now defined as ~2|2|...2 with 2|2 instances of 2, left associative, I find it hard to specify how large the subscript on the “f” notation would be. And this is just the smallest possible multiple bar number, with numbers like 3|||3 being incomparably larger. If the fast-growing hierarchy can reach TREE(3), then why can't this set of functions which iterate their own functional recursions, do so also? Thank you for reading and for thinking about this.