> If, however, a and b are dates, these operations are nonsensical
If you encode dates as number of days since some fixed date, they can be seen as numbers on a timeline, so the start date and the length (in days) of a "date interval" could be useful information. If you mean that subtracting two dates represented as strings of "YYYY-MM-DD" form is nonsensical... well, duh.
> for date range comparisons it is much more understandable to use start-of-day on a and end-of-day on b
I personally agree with this, but then again, "more understandable" is a subjective notion. I don't see how it make open intervals for dates nonsensical in itself.
"You're arriving on 15th and going home 23rd" implies that you're there 23-15=8 full days (unless we count the arrival/departure half-days as full days, in which case the arithmetic itself breaks down, so it doesn't matter which intervals we use mathematically) - that's an open interval.
Encoding dates in data in any other way than native date datatypes or full ISO date/timestamp strings is incredibly dangerous and prone to tz and dst conversion issues. It still might fit some niche use though. I was thinking more in line with some sort of Date entities.
Your example, as you point out, is flawed with respect to reality: no system would record arrival/departute dates and expect to calculate accurate length of stay, except in full days, as in b-a-1 = 7 days, effectively making the example use a closed interval if it were implemented in reality.
Imagine a hotel reservation system using just dates. Arrival on the 15th and departure on the 23rd would mean a reservation from the 15th to the 22nd, while the 23rd would already be free for someone else to book.
If you encode dates as number of days since some fixed date, they can be seen as numbers on a timeline, so the start date and the length (in days) of a "date interval" could be useful information. If you mean that subtracting two dates represented as strings of "YYYY-MM-DD" form is nonsensical... well, duh.
> for date range comparisons it is much more understandable to use start-of-day on a and end-of-day on b
I personally agree with this, but then again, "more understandable" is a subjective notion. I don't see how it make open intervals for dates nonsensical in itself.
"You're arriving on 15th and going home 23rd" implies that you're there 23-15=8 full days (unless we count the arrival/departure half-days as full days, in which case the arithmetic itself breaks down, so it doesn't matter which intervals we use mathematically) - that's an open interval.