User blog comment:MilkyWay90/Help with understanding Veblen array notation/@comment-30754445-20180811202716/@comment-35392788-20180819140004

I was just pointing out some stuff, I don't think I got offended by your post.

As for UNOCF allowing exponents inside the psi, that's mostly a way to make thing prettier. Every UNOCF expression (up to I) can be expressed using psi function, 0 and addition. So, really, \(U(\Omega^\Omega)\) is notation sugar for \(U(U_1(U_1(U_1(0))))\), and \(U(\Omega^{\Omega+1}) = U(U_1(U_1(U_1(0))+U_1(0)))\).

I'll see if I can try to redefine UNOCF in a clearer way, but, in the meantime, let's just bury this conversation.