User blog comment:Kyodaisuu/Mashimo function/@comment-24509095-20140705233241/@comment-1605058-20140706065057

\(CKF(20)=\omega^{CK}_{CKF(20-20)}=\omega^{CK}_{CKF(0)}\omega^{CK}_1\). So this function is total (as far as I know there is no notion of continuity for functions taking arguments from N, so I guess you meant totality).