User blog comment:Triakula/Uncomputable functions defined as a sequence of computable functions/@comment-35470197-20200131231857/@comment-35470197-20200201060308

I see. Thank you. For example, if you define g_n:N→N by f_{i_n} and i_n∈N by then the resulting hierarchy (g_n)_n actually eventually dominates all computable functions. If you want an actually uncomputable function by diagonalising them, you need to define h(n) = g_n(x(n)), where x(n) = min {x∈N|g_n(m)>f_j(m),∀m≧x,∀j≦i_n} or something like that.
 * 1) i_0 = 0 and
 * 2) i_{n+1} = min {i∈N|f_i >* f_j, ∀j≦i_n},