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I searched for this, but all I found was an English usage result. However, I am strictly asking about ranges of numbers, not "normal" English.

So, are there a terse terms for:

  • inclusive between, as in 1 is between 1 and 5
  • exclusive between, as in 3 is between 1 and 5, but 1 is not

Maybe something sporty like exobetween and endobetween?

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JamesFaix
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    Mathematicians often distinguish between open intervals that do not contain the endpoints and closed intervals that do. The use of round and square brackets convey this information succinctly, and also allow one to quickly convey when one endpoint is included and the other excluded. – hardmath Jul 19 '16 at 03:44
  • I'm actually looking for an answer to use for naming functions in a programming library. This eliminates the possibility of () and [], which do work wonderfully in print. However, the words "open" and "closed" might do the trick. The function names "BetweenOpen" and "BetweenClosed" aren't too bad. – JamesFaix Jul 19 '16 at 03:59
  • Are you thinking of functions that test for arguments to belong to such intervals (open and/or closed)? – hardmath Jul 19 '16 at 04:53
  • @hardmath Exactly. For situations like checking that a given array index is between 0 and the length of the array minus 1. In a language like Java, it would be a function like bool IsBetweenClosed(int value, int min, int max) {return value >= min && value <= max;} I just want to keep the function names and short and intuitive as possible, as this is really simple conceptually. – JamesFaix Jul 19 '16 at 12:17
  • Speaking or writing informally, I might say “strongly between” and “weakly between”. – Lubin Jul 19 '16 at 17:21
  • I guess you could say "properly between" or "strictly between" and most people would probably be able to work out what you mean. But that only handles one case. "Improperly between" and "nonstrictly between" sound stupid. P.S. All the repetitions of "between" in the question and comments make me realize what a weird word "between" is, like some kind of relic from Olde English. –  Jul 19 '16 at 17:35
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    @Bungo, I'm starting to get that olde vibe myself. Maybe we should go with between vs asandwich'd – JamesFaix Jul 19 '16 at 18:45
  • To address @Bungo's concern about the stupid sounding versions (a view I agree with), maybe "strongly between" and "weakly between"? – Dave L. Renfro Jul 19 '16 at 20:27
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    I'd suggest: between=openbetween= $1 < x < 5$. closedbetween = $1 \le x \le 5$. leftbetween= $1 \le x < 5$ and rightbetween $1 < x \le 5$. – fleablood Jul 19 '16 at 20:29
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    tweens don't do a lot of math, so I suppose they don't much care. It seems like an open and closed case to me. –  Jul 22 '16 at 19:10

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Although not as sporty as "endobetween" and "exobetween", mathematicians generally use the adjectives "closed" and "open" to describe the inclusion or exclusion of endpoints in an interval (range) of real numbers.

Thus $(0,1)$ is an open interval, excluding (not containing) the endpoints, and $[0,1]$ would be the corresponding closed interval resulting from including both endpoints.

Another paradigm from mathematical terminology would be that used of inequalities, namely strict (excluding the boundary/equality) or weak (including the boundary/equality). Thus IsBetweenStrict should be expected to reject the endpoints, while IsBetweenWeak should be expected to accept the endpoints.

hardmath
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    I would take this opportunity to coin the pseudo-Greek "aperintervalic" for "of an open interval", but the corresponding "cleistrintervalic" sounds like one's grinding one's teeth. – JamesFaix Jul 19 '16 at 19:01
  • @JamesFaix: On behalf of us Attic coders everywhen, I thank you. – hardmath Jul 19 '16 at 19:12