Suppose we are talking about the numbers 1, 2, ... , 10.

When we use the phrase between 1 and 10, do we include the end-points 1 and 10? Is there any difference if we say from 1 to 10 instead?

  • I'm sure if I say "Pick a number between 1 and 5", well over 60% of the responses will be between 2 and 4. But I don't think that's because people assume 1 and 5 aren't valid choices - it's just the tendency to go for somewhere "in the middle", when faced with such choices. – FumbleFingers Aug 21 '12 at 1:10

Saying “between 1 and 10” is somewhat ambiguous; usually people will say “between 1 and 10 inclusive” or “between 1 and 10 exclusive” to clarify when there is no other context. Both “between…and…” and “from…to…” are usually considered inclusive unless otherwise specified.

  • This is spot on, though I would qualify it by saying that the particular example you chose (1-10) as well as 1 to other common round numbers (e.g. 1-100) are very commonly inclusive, especially when rating things or picking random numbers. For that reason, I would interpret both Pick a number between 1 and 100 and Rate this hotel from 1 to 10 to be inclusive, absent any clarifying context. – Dusty Jan 3 '11 at 17:16
  • @Dusty: Right you are. Updated. – Jon Purdy Jan 3 '11 at 17:20
  • @Jon-Purdy You might want to edit to specify "Both phrases (between 1 and 10 and from 1 to 10) are usually considered inclusive..." since you mean to refer to the OP's two examples, right? (I thought "both" referred to your inclusive/exclusive examples at first, and was a bit confused.) – aedia λ May 23 '11 at 17:26
  • @aedia: Done and done. – Jon Purdy May 23 '11 at 20:56

For whatever it is worth, the SQL meaning of WHERE a BETWEEN x AND y means the same as WHERE a >= x AND a <= y, so it is inclusive of the end points.

Most people, most of the time, will interpret 'between 1 and 10' or 'from 1 to 10' as including both end points. In the absence of any indication to the contrary, both the end points will be included.

Mathematicians like half-open ranges that include the start and exclude the end; there are some benefits to that notation.

So, until the world changes its attitude towards the terms, you will have to explicitly qualify 'between 1 and 10 exclusive' to obtain your desired result - and expect to confuse people even with the qualifier, at least in spoken communications. That is, if you ask a kid to choose a number between 1 and 10 exclusive, expect them to choose either 1 or 10 about 20% of the time.

  • does "between 1 and 10, exclusive" exclude only 10 or both 1 and 10? How do we differentiate between those cases? – Mr. Shiny and New 安宇 Jan 6 '11 at 19:36
  • 1
    As written, 'between 1 and 10, exclusive' would exclude both end values (and would be better written as 'between 2 and 9' or '2 to 9'. 'More than one, up to ten' and 'One or more, but less than ten' would cover the two half-open ranges reasonably unambiguously, as would '2 to 10' and '1 to 9'. I've mixed numbers and words horribly in the answer -- oops! – Jonathan Leffler Jan 6 '11 at 19:41

If you want to exclude, then at least for integers you could say:

  • Between 2 and 9 (so that when interpreted in the "inclusive" sense, this contains the range 2--9, inclusive of the endpoints)

  • From 1 to 10

This way, even though you cannot change the language, you can change the statement to get the desired effect (without using the word "inclusive")

(Btw., the above solution is aesthetically displeasing due to the implicit asymmetry)