User blog comment:Dchew89/General Idea for my d(n) Function/@comment-35470197-20190306060453/@comment-38080588-20190306062125

Well, the given example is not supposed to be well defined. If I wanted to give a trivial well defined sequence I could say that the FS of \(\omega\) is \(sup\{0,1,2,...\}\) and the FS for \(\varepsilon_0\) is \(sup\{\omega,\omega^\omega,\omega^{\omega^\omega},...\}\). Then the sequence would be \(d(0)=0;d(1)=1;d(2)=2;d(3)=\omega;d(4)=\omega+1;d(5)=\omega+2;d(6)=\omega2;d(7)=\omega^2;d(8)=\omega^\omega;d(9)=\varepsilon_0;...\)