User blog comment:MilkyWay90/Help with understanding Veblen array notation/@comment-30754445-20180811202716/@comment-30754445-20180819133027

My point was to explain things as clearly as I can to MilkyWay90 and Fefjo, while clearing any possible points of confusion. And one of these points of confusion is that people who are only familiar with UNOCF expressions would not understand why my examples (given in standard notation) are "wrong".

I've also went to great lengths to try and avoid precisely the kind of argument you're now dragging me into. Did you notice that I specifically said that UNOCF does precisely the same thing up to the BHO, with the sole difference of counting multiples of omega rather then epsilon-numbers? Did you also notice that I've completely glossed over the fact that UNOCF is technically ill-defined, specifically to avoid this silly confrontation?

Actually, I've also glossed over the fact that UNOCF doesn't even do what I (or you) claimed it does. It is a strange hybrid. On the one hand, it counts multiples of omega. On the other hand, it allows for exponents inside the ψ function. So no, it most certainly isn't a direct parallel to ordinary OCFs that just replaces "closed under exponentiation" with "closed under addition". It's something else.

Of-course there's nothing wrong with being "something else". But I knew that if I wrote something like that, people like you would get all defensive again. So I glossed over that detail (which wasn't important to my explanation anyway). Yet somehow, incredibly, you still found a way to get offended by my post.

Now, can we get back to the topic of the discussion here (which - to remind you - has absolutely nothing to do with UNOCF)? Sheesh...