User blog comment:Googology Noob/Ordinal FGH, with an actual definition!/@comment-1605058-20151219200302

"...f_beta(w), and the ordinal resulting would be larger [than beta]." I don't see why it should be true. Indeed, it seems to me that the function $$\alpha\mapsto f_\alpha(\omega)$$ can be (assuming all the necessary FSs are defined) normal (increasing and continuous), and this would mean that it has a fixed point.