Comment by brabel

Don't you see that what you're talking about is a range, not counting?? A range indeed starts at a zero point because if you don't have another point, you just have an empty range: and that's the equivalent of a zero range. When you have two points in a range, then the "first" point ends up being zero, that's correct, because it's being treated as the beginning of it. An "origin" is always associated with zero. It's perhaps incorrect to use the word "first" in this case exactly because it "breaks" how ordinals actually work (i.e. 1=first, 2=second, etc.). A better word is the "initial" point of a range, and the "other" point is the "final" point. Each segment you consider will be a pair [initial, final]. Here's where your mistake comes in: you assume that you can just take each segment and assign it a single number, but instead of using the ordinal numbers which start from 1, you decided to, arbitrarily, take the initial point of the range as your number instead, which is where the zero comes from. Notice that the zero you chose comes from the pair [initial, final], but the zero only makes sense when it's in a pair (alone, zero means the absence of something, i.e. there's no range... I thought that concept was well understood at least by fellow programmers, but apparently not).