What is the symbol “between” (≬) used for?

The `amssymb` package has a binary relation symbol named `\between`, which I have never come across.

What is it used for?
I found out from a compiler error when I tried to define a symbol named that way myself, and I am now wondering whether it is a symbol I could use for my purpose.

• I wonder if there is any efficient way to find all ArXiv papers that contain `\between` in their Latex source code? Nov 1, 2010 at 9:23
• This is an interesting question, and I'm curious to find the answer, but I can't help it would be better placed at the mathematics stackexchange: It's not really a question about LaTeX... math.stackexchange.com Nov 1, 2010 at 11:39
• Never seen it before. It's in unicode, though: fileformat.info/info/unicode/char/226c/index.htm Nov 1, 2010 at 14:15
• @Caramdir: Thanks for the edit! (new at this..)
– Alright
Nov 1, 2010 at 16:48
• That's a closing parenthesis telling the open parenthesis "If I'd be any closer to you I'd be behind you" :-) May 22, 2022 at 1:34

I found it in the Journal of Combinatorial Optimization (2007) 13:217-221, February 14, 2007: A 2-approximation for the preceding-and-crossing structured 2-interval pattern problem. There the expression `\{<,\between\}` has been used, as can be seen in the abstract.

Regarding intervals, `\between` may stand for a crossing/overlapping relation like < for a precedence order and kind of a subset symbol for inclusion/nesting. See also Extracting constrained 2-interval subsets in 2-interval sets.

In such difficult cases, the LaTeX search engine of Springer is a useful tool (now discontinued).

• That's quite a lot of definitions given in a short 5 page paper. @Stefan: how did you actually perform this feat of finding where a symbol is used? Nov 1, 2010 at 15:35
• @Willie: I used Google Code search. Nov 1, 2010 at 15:57
• @Alright @Willie: I used the Springer LaTeX search. I will add that to the answer. Nov 1, 2010 at 19:34
• Once found the relation to intervals, google image search (for interval subsets or 2-intervals) restricted to tiny images immediately gave the other result. Other ways to try in general might be google with options filetype:tex and perhaps additionally site:arxiv.org. Nov 2, 2010 at 12:11
• Briefly, given two intervals I = (a,b) and J = (c,d), there are (barring coincidences) 6 possible relative orders of a, b, c, and d, giving the 6 results I < J, J < I, I ⊏ J, J ⊏ I, I ≬ J, and J ≬ I, with the symbols to be read ‘precedes’, ‘is nested in’, and ‘crosses’ (not ‘is between’). Nov 30, 2016 at 18:56

It is not new. It appears on page 28 of "Kummer's quartic surface" by R W H T Hudson (Cambridge University Press 1905, republished 1990; WorldCat) without explanation, so was presumably well understood by Projective Geometrists then.

It was used by Hudson in "Kummer's Quartic Surface" to denote the inner product of two single-row matrices, for instance (a,b,c,d≬x,y,z,t) = ax+by+cz+dt. The advantage of the notation seems slight and may merely have saved space by not having to write the second matrix as a vertical column in the usual way.

• Further to my last note, it was used by Hudson in "Kummer's Quartic Surface" to denote the inner product of two single-row matrices, for instance (a,b,c,d≬x,y,z,t) = ax+by+cz+dt. The advantage of the notation seems slight and may merely have saved space by not having to write the second matrix as a vertical column in the usual way. Nov 24, 2012 at 15:03
• The notation goes back to Cayley, see tex.stackexchange.com/q/487643/4427 Dec 10, 2020 at 9:24

It's a mathematical symbol. I use ≬ in genealogy. Dates are often imprecise. The widow's husband dies in 1780 and she is listed as deceased in her son's marriage bond in 1799. So she died ≬1780-99.

In constructive mathematics and pointfree topology, "AB" means that the sets A and B have an element in common. Constructively, this condition is stronger than merely stating that the intersection AB is not empty, and appears in many places. Hence it makes sense to have a special symbol for it.

I don't know who introduced this notation, might be Giovanni Sambin, but in any case Peter Schuster and Daniel Misselbeck-Wessel are often using the symbol in their papers. To cite just one example: Eliminating disjunction by disjunction elimination

• I might ask Peter: his office is two doors from mine. Feb 9, 2023 at 22:26
• Peter Schuster answered to my mail: he says to have taken the symbol from Sambin's papers (by the way, Sambin was one of my teachers during the PhD), but that he's pretty sure to have seen the symbol also in some short paper by Ore, maybe with the same meaning. Feb 10, 2023 at 11:01

I have never seen it before so I'm not sure where it comes up. That said, as long as you define your symbols, you can use them for whatever purpose you want. People might be confused if you redefine + as -, but I suspect that `\between` is sufficiently specialized that you can repurpose it as you wish.

• I know. But I usually try to come up with as little new notation as possible. And the name of the symbol is suggestive enough to make me wonder whether other people already have a notation (that symbol) for the same thing.
– Alright
Nov 1, 2010 at 16:45