User blog:MachineGunSuper/Updated Exploding Fast Growing-Hierarchy

So, some while ago I uploaded "The Exploding FGH", which after \(\omega * 2\) was a complete failure. But then, I had barely any idea of what \(\varepsilon_0\) meant in the FGH, but now I am very documented and understand all of it.

Rules
\(₰_0 (n)\) = \(f_0 (n)\) = n+1 

\(₰_1 (n)\) = \(f_1 (n)\), but instead of being iterated n times it is n+1 times.

\(₰_a (n)\) = \(₰a-1 (₰a-1(₰a-1(...(₰a-1(n))...)), with ₰a-1(n) iterations)\)

First few values for the imput being 3
\(₰_0 (3)\) = 4

\(₰_1 (3)\) = 7 ; \(₰_1 (n)\) = n+n+1

\(₰_2 (3)\) = 511

'''\(₰_3 (3)\) = ₰2(₰2(...(₰2 (3)))..)), with 511 ₰ 2's

Ordinals
\(₰_\omega (n)\) = \(₰_n (n)\)

You know how to go from here, it's just like with the FGH. There are the absolute same fundemental sequences, just diagonalize and pick the n-th element. The only different rules are those with the iteration differences.