[goto11]

You may be right, but in that case, why is the second range "nicer"? AFACT it is because he explicitly adds 1 in the first example but implicitly subtract 1 in the second, which makes it looks cleaner. If you want the N'th element of an array, the range in the first example is N ≤ i < N+1 while in the second it is N-1 ≤ i < N. Written out like that, I don't see how the second is obviously nicer.

[kbd]

Sure. Something is generally considered more elegant ("nicer") when it has fewer terms. (I'm really happy with my own argument above why Python's indexing is "optimal".) But I'd put what I think you're saying this way: Dijkstra asserts that '1 ≤ i < N+1' is worse than '0 ≤ i < N', but he's choosing his conditions carefully. '1 ≤ i ≤ N' also has no extra terms. (Though in fairness to Dijkstra, this section was after he'd already argued why closed, open ranges are better.)

I will say this though: in all the noise in this sub-thread, I never got any example in answer to my original question asking for any algorithm or formula that works out better with 1-based indexing (my original response was to its parent's claim that 1-based indexing results in fewer ±1s in practice). Except for maybe the "stride" examples[1] for which I still don't understand why the starting index is important. I say this not in victory (ha ha! zero-based indexes are clearly superior!) but in disappointment because I was hoping to gain understanding of why Julia/Matlab and others (which are more geared towards math/stats which is outside of my experience) made their indexing choice. Particularly because it's against the norm, they must have good reasons.

[1] https://news.ycombinator.com/item?id=20425500

[goto11]

I'm actually arguing the opposite, that 0 ≤ i < N does have an extra term - it is just hidden! Where does the zero come from? The generalized form for picking the N'th number (with zero-based indexing) is N-1 ≤ i < N. So the 0 is N-1 which have been simplified because you know N is 1. But in that case couldn't you also just reduce the terms in the example with 1-based indexing similarly? Reducing the term in the one example to make it simpler is just cheating.

I'm not disputing the choice of closed-open rage, but I'm arguing the expressions are equally simple with either 1 and 0 based indexing.

As for an example where 1-based indexing is better, I had such an example in a another subthread: Translating between the numbers and names of months. Or indeed anywhere where you have a list of things and you want to pick them by ordinal numbers. E.g if you want the N'th president, it is simper to do presidents[N] than presidents[N-1].