User blog comment:Googleaarex/Extended HyperNested Arrays/@comment-25418284-20130407213804/@comment-1605058-20130408132128

@FB100Z Given any collapsing function which is everywhere nondecreasing and continuous, suppose it doesn't happen to be constant after some point. So, for every ordinal \(\alpha\) such that \(f(\alpha)=\gamma\) there is an ordinal \(\beta\) such that \(f(\beta)>\gamma\). Define \(F(\alpha)\) to be smallest such ordinal. Construct a set containing 0 and closed under and \(F\) and countable limits. This is analoguous to countable ordinals, so this set is uncountable. So \(f\) maps to uncountable set of ordinals. But every collapsing function is a notation, thus bounded by CK ordinal, thus countable. Contradiction