User blog comment:Plain'N'Simple/A question for proof-theory experts/@comment-38817512-20191103200212

X(n) seems to be uncomputable. Yes, the functions in K(n) are computable, but as we increase n, it doesn't look like there is a way for a turing machine to choose the fastest. On the other hand, E(n) is a function in FGH, so it is computable. I'm not sure about this, but i think uncomputable functions are generally stronger than computable functions, so X(n) will overgrow all computable functions, including f_e0(n).