User blog comment:Deedlit11/Extending the fast-growing hierarchy to nonrecursive ordinals/@comment-25418284-20130318051254/@comment-25418284-20130318054044

Ah, I get it now. Thanks. Depending on the ordering we pick, the fundamental sequence and thus \(f_{\omega_1^\text{CK}}(n)\) will change &mdash; but, to paraphrase Conway, it's so big it doesn't really matter. Its rate of growth stays the same, and that's what's important.