User blog comment:Edwin Shade/Can Chess Ordinals Produce Functions With Uncountable Growth Rates ?/@comment-1605058-20171222153040/@comment-32876686-20171222160859

You are correct, but if I may ask, why precisely can't I consider \(\omega_1^{{\mathfrak{Ch}_{\!\!\!\!\sim}}_3}\) as the supremum of \(\mathfrak{Ch}_n\) ? (At least in a hypothetical sense, for though I am aware \(\omega_1\) has no fundamental sequence, isn't my function well-defined.)