User blog comment:B1mb0w/Mapping D(l,0,1) to epsilon nought/@comment-1605058-20150702203134/@comment-68.186.6.2-20150731150710

It seems he thinks that $$f_{\omega+1}(n) = f_{n+1}(n)$$ just because $$f_{\omega}(n) = f_{n}(n)$$ - for example he thinks $$f_{\omega+1}(3) = f_{\omega}(f_{\omega}(f_{\omega}(3))) = f_{3}(f_{3}(f_{3}(3))) = f_4(3)$$. $$f_{\omega+1}(3)$$ instead means $$f_{f_{f_3(3)}(f_3(3))}(f_{f_3(3)}(f_3(3)))$$. See, iterating the $$f_{\omega}$$ function isn't the same as iterating the $$f_n$$ function, but iterating the position of functions in the finite fast growing hierarchy!