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Semi-open intervals ([a,b), where xbelongs to the interval iff a <= x < b) are pretty common on programming, as they have many convenient properties.

Can anyone offer a rationale that explains why SQL's BETWEEN uses a closed interval ([a,b])? This is esp. inconvenient for dates. Why would you have BETWEEN behave like this?

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I'm curious, what convenient properties do they have? –  phant0m Aug 9 '12 at 18:51
if it was not inclusive how could you easily query for all last names in the range A to D? or names W to Z? For numbers between 1 and 10 you can search 0 < n < 11, but for characters you would have to use ASCII numbers? or unicode numbers? Plus, the indexes can easily get you to the start of your data. –  james Aug 9 '12 at 18:58
I understand your frustration, (StartDate >= '2010-01-01' and StartDate < '2011-01-01'), works beautifully, to use Between the equivelent would be (StartDate between '2010-01-01' and '2010-12-31 23:59:59'), both bulky and one needs to know how many days are in Dec. –  Todd Jan 17 '13 at 0:31
@phant0m [a,b) U [c,d) == [a,d). [a:int,b:int) contains exactly b-a elements. Todd's comment shows how they work especially well for dates (which is were I miss them most). Basically, when coding, semiopen intervals tend to be simpler, easier to use and robust. –  alex Jan 17 '13 at 20:53

3 Answers 3

up vote 20 down vote accepted

I think inclusive BETWEEN is more intuitive (and apparently, so did the SQL designers) than a semi-open interval. For example, if I say "Pick a number between 1 and 10", most people will include the numbers 1 and 10. The open-ended interval is actually particularly confusing for non-developers because it's asymmetric. SQL is occasionally used by non-programmers to make simple queries, and semi-open semantics would have been much more confusing for them.

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Your example focuses on integers, for decimal numbers and other delimited quantities (such as dates), the term between is ambiguous. If I say have you done X between 2012 and 2013, I don't include 2013 (or specifically the day 2013-01-01) –  Todd Jan 17 '13 at 0:35

Both inclusive (a <= x <= b) and exclusive (a < x < b) are about equally common, so when making the standards they simply had to pick one. "Between" in common English is typically inclusive, and a SQL statement is meant to read similar to an English sentence, so inclusive was a sensible choice.

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The operator isn't called ∩[a,b), it's called BETWEEN, so it's considerably more appropriate for its semantics to be those of the English phrase "is between" than those of the mathematical predicate "is in semi-open interval".

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