User blog comment:P進大好きbot/Please Help me on study of Pair Sequence System (2-rowed Bashicu Matrix System)/@comment-35870936-20180813215517/@comment-35392788-20180815073904

Well, I don't think there are any detailed comparisons between KOCF and UNOCF, but it's not hard to compare them.

It is pretty clear that \(\psi(\varepsilon_{\Omega+1}) = U(\varepsilon_{\Omega+1})\). In KOCF, this can be written as \(\psi(\psi_1(0))\), while in UNOCF, it's \(U(U_1(\Omega_2)) = U(U_1(U_2(0)))\). Likewise, \(\psi(\psi_1(\psi_2(0))) = U(U_1(U_2(U_3(0))))\)

In KOCF, \(\psi(\Omega_\omega) = \psi(\psi_1(\psi_2(\ldots)))\)

In UNOCF, \(U(\Omega_\omega) = U(U_1(U_2(\ldots)))\)

Since we can find an equality between UNOCF and KOCF at every step of the abovementioned fundamental sequence, we conclude that \(\psi(\Omega_\omega) = U(\Omega_\omega)\)