User blog comment:Edwin Shade/Defining LOCC (Language Of Ordinal Construction)/@comment-32697988-20170924234138/@comment-32697988-20170925211016

Addition, multiplication and exponentiation are defined for ordinals, but ordinal tetration is not defined yet. So, if you want to include tetrationin your definition of LOCC/LOOC, you have to define tetration first. Just saying that a^^1=a, a^^(b+1)=a^(a^^b) and (a^^b)[n]=a^^(b[n]) is wrong: if you use it, w^^a will get stuck at e0 because w^^w=e0 and w^^(w+1)=w^(w^^w)=w^e0=e0, w^^(w+2)=w^e0=e0, etc.