User blog comment:Scorcher007/About Cofinality, sipmly/@comment-35470197-20190722064020

I think that it is better to teach ordinals restricted to the countable realm, because even \(\omega_1\) is very difficult for beginners. If one understands properties of \(\omega_1\), e.g. the non-existence of a countable fundamental sequences, then it might be good to talk about classifications of ordinals below \(\omega_2\) by the least "length" of fundamental seqences, as an analogue of the classification of countable ordinals into zero, successors, and limit ordinals.