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.
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Don't get me started on off by one. I'll never get indexing straight! lol
But obviously everything should start indexing at zero!
The constructivist (i think that's the term, i just learned it) school of philosophy/math, doesn't see any proposition or its negation as necessarily the only possibilities. This is unusual since all the math and reasonsing we do typically assumes this implicitly. There's a term "law of excluded middle" that is related, you can sorta guess what it means.
In this vein, there were issues with infinity/real numbers (infinite sequences lead to irrational numbers) a 100-200 years ago, which went glossed over for a long time, but finally had to be tackled, and that's partly what led to for example the Dedekind construction of the real numbers. It lays out a concrete canonical definition of what they are set-theoretically. You might enjoy a look into that.
