Sorry "basal number" is something I just made up, I was trying to describe "numbers of a number system that uses a base". I thought I could save myself some writing, but I got too cute with it lol.

To me, unary seems like just the special case. For all positional number systems, as the base approaches 1, the number of irrelevantly-positional numbers predictably increases until it reaches 100%. It fits a pattern. And in a more meta view, 1 is a pretty common "special" or "trivial" case, along with 0, and infinity. I think it's a bit strange to say it doesn't belong in the set.

I'm not quite at the point where I'm gonna read a math book for fun, but there are these little pieces of math that are fascinating.