makin me open notedeck to keep up with your gd fast typing. you're confounding slightly, i think, expressing numbers in a system (whatever base you choose), vs defining things with a more general language. At least that seems to be one of the issues. I fully understand how you can do larger numbers with fewer slots in a really high-base system, that's clear. This sort of thing comes up when you try to closely analyze "propositions" in math, and I'm not equipped to really go any deeper, just a tourist still.

yeah, zero drives me crazy. in computers, zero stands in for first, so you use one encoding, and have two semantics, cardinal (counting) and ordinal (sequence). this is why off-by-one bugs are very common in iterator code. the fact that computers encode everything as binary also gets quite confusing because of the way that AND/OR/NOT/NOR/XOR operations can happen, but they make changes in the values that don't comport to "normal" arithmetic operators. and multiply and divide themselves are essentially adding a dimension on top of their base. idk... anyway, that's the thing about arithmetic. it is about space and time, and counting. that's where the "met-" part comes from in the name because it's based on counting. and rhythm too, which is also about counting, and time.