User blog comment:Ikosarakt1/Extensions of Catching function/@comment-35470197-20200118085643

As LittlePeng has already pointed out at the comment page on hyp cos's original article, Catching function is ill-defined unless you fix a system of fundamental sequences for all countable ordinals (or a sufficiently large ordinal beyond the "limit" of the corresponding Catching function itself.) Even C(0) does not make sense, although people often assume that it is ψ(Ω_ω).