User blog comment:MachineGunSuper/The Listaments 5/@comment-32876686-20180111210626/@comment-34434829-20180124210740

I'm sorry,  MGS, but Edwin is 100% correct in both of his statements.

Creating an infinite list of functions is not sufficent to dominate all computable functions. A classic example is f_w(x) which dominates f1(x), f2(x), f3(x)...

Even worse: It can be shown that no such list can be built by nesting functions. The dream of such a "catch-all" system is a theoretical impossibility. It simply can't be done, period.

Also, what Edwin means by "confusing" is that you haven't properly defined your functions. There are gaps in your descriptions. There are too many ambiguities and points of unclarity as to what we should do next.

Since you have a clear idea of how the system should work in your head, you  can fill these gaps without problems. We, the readers, can't.