User blog comment:LittlePeng9/Long hierarchies of functions (on my other blog)/@comment-11227630-20171031155258/@comment-1605058-20171107185655

We are not talking about "length", we are talking about cardinality. What matters is that there is a bijection from \(\omega_1+1\) and \(\omega_1\), taking \(\omega_1\) to \(0\) and every other ordinal \(\alpha\) to \(1+\alpha\).