User blog comment:KthulhuHimself/Ordinal Arithmetic Notation (OAN)/@comment-35470197-20191112141154/@comment-35470197-20191117103416

> By defining larger ordinals using only successors and limits of sequences of smaller ordinals defined in this very same system, we allow the notation to rely entirely on arithmetic and layers of recursion.

...Do you know the definition of the computability? According to what you said, you seem to comfound the notion of a computable function with that of a function which can be computed in a repetition of aplications of elementary operations. The latter one has nothing to do with the computability.