I think other languages aimed at mathematicians, like Julia[1], do this for similar reasons but, honestly, unless you're writing a CAS, I think it's a bad idea.
Having lived with Dijkstra's ideas for a while, I will say that people find closed-open sequences highly counter-intuitive.
I work on a financial simulator, so we use dates quite a bit. Representing a year as 1-Jan-X up to but not including 1-Jan-(X + 1) is perfectly natural, and really works well with date-time libraries. It still works if you're using dates and decide to extend it to handle datetimes, and even months 1-M-X to nextmonth(1-M-X) do what you'd expect. So he's right, the math works beautifully. You also avoid writing a successor function when you split closed-open ranges; easy with integers, but gets tricky with almost anything else.
But I've had to nag people many times to not use Dec 31. I think the intuition for a closed-closed ranage is deeply ingrained and that extra "Jan 1" seems to stick out and bother people.
From that discussion, here's an interesting argument in favor of 1-based indexing:
> Let me try to briefly convey how I learned to stop worrying and love 1-based indexing. Basically it comes down to the fact that there are three significant numbers you have to think about when it comes to an array: it's initial index, final index, and length. In 0-based indexing, these are all different: 0, n-1, and n. In 1-based indexing, the final index and length are the same: 0, n, n. That's one less thing to think about and keep track of when coding. It seems trivial, but when you're doing something tricky and juggling a lot of complicated things in your head, even the tiniest alleviation of cognitive load helps, I find.
[1]: https://groups.google.com/forum/?hl=en#!topic/julia-dev/tNN7...