Ripheus23

I feel like there must be different levels of xatrix functions. Like, in one case you infinitely compound the hypertower's two indexes by the HT's own form. That's maybe the smallest. I actually don't know the counterpart sigma-function case (aleph-zero ^(aleph-zero) aleph-zero ^(aleph-zero)...) for the predecessor to the counterpart xatrix-sigma arithmetic, so although I think the basic xatrix hypertower goes to (omega.1)aleph-zero, I don't know how much further the sigma-case goes, here.

But anyway, compounding the glyphdex and converting it into a series of xatrix hypertowers has to go farther, for the sake of the fact that the simplest aleph-case of a hyperglyph [((aleph-zero)aleph-zero)aleph-zero] already goes farther than the simplest xatrix hypertower (on my occurrent assumptions).

The next major question of form of levels, then, (that I have anyway...) is what happens when we have a xatrix with more than one kind of variable? Like, I've started with ones where all the variables are X, but we could have ones with X and Y, or ones with countably or uncountably many variables? In that event, taking the xatrix function of such a system seems as if it would have to go to some realm of continuously branching levels, even if each level is, inside of itself as such, countable? I don't know. Technically, I still don't have a clear enough presentation of transfinal arithmetic, which is what I'm working towards...