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\begin{align} \forall x\in(0,+\infty), \quad f(x) > 0 \tag 1 \\[10pt] \forall x\in ]0,+\infty[, \quad f(x) > 0 \tag 2 \\[10pt] \forall x\in {]}0,+\infty{[}, \quad f(x) > 0 \tag 3 \end{align} I was instructed from an early age to use the notation in line $(1)$ above. In France apparently the one in line $(3)$ prevails, or at least has some currency. I coded line $(3)$ like this:

\forall x\in {]}0,+\infty{[}, \quad f(x) > 0

Line $(2)$, on the other hand, is coded like this:

\forall x\in ]0,+\infty[, \quad f(x) > 0

In the conspicuous difference between the appearances of lines $(2)$ and $(3)$ we see that MathJax doesn't apply the spacing conventions that it applies well in line $(1)$. (Apparently to some users this is not conspicuous until the actual juxtaposition of lines $(2)$ and $(3)$ is seen.)

If one must use the French notation, how should that be done? Just the way I did in line $(3)$? Or is there a less crude way?

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    $\begingroup$ I don't know, but it might be worth trying \left] and \right[ to see if that improves the spacing. $\endgroup$ – hardmath Dec 1 '16 at 20:03
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    $\begingroup$ This might be a good question for the TeX SE $\endgroup$ – Omnomnomnom Dec 1 '16 at 22:51
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    $\begingroup$ I don't spend much time on Meta, and no offense to the OP, but why is this not considered off topic? Typically people on this site are like hawks about that kind of thing... $\endgroup$ – The Count Dec 2 '16 at 2:46
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    $\begingroup$ FWIW we (i.e. in Finland) use that notation in schools. When meeting a fresh batch of college kids among the first things I teach them is the ``proper'' notation for intervals. 'cause this is ugly as (insert unflattering comparison of choice). I sorta see the point of using this in schools, because $(a,b)$ is one of the more overloaded pieces of notation. But, imagine typesetting a union of a mixture of open/half-open intervals (I am sparing your eyes). $\endgroup$ – Jyrki Lahtonen Dec 2 '16 at 5:35
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    $\begingroup$ @TheCount How could this possibly be off-topic? It is a question about how to typeset something correctly/conveniently on this site. What would be off-topic are (La)teX questions (see TeX - LaTeX for this) and also general queries on MathJax (like, 'How to I configure MJ for my blog?'; yet this can go to Stack Overflow AFAIK, the main site of course not its meta) $\endgroup$ – quid Dec 2 '16 at 9:19
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    $\begingroup$ @JyrkiLahtonen I quite disagree on this, but that's off-topic. It's also not clear why it is "proper." And as we are talking about doing things properly and things being ugly, ``proper'' is extremely ugly here as LaTeX syntax does not work on this site. ;-) $\endgroup$ – quid Dec 2 '16 at 9:34
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    $\begingroup$ @quid, yes, the output in LaTeX is the same as MathJax for all three lines above. So asking about this on TeX - LaTeX (without mentioning MathJax) should be on-topic there. $\endgroup$ – Davide Cervone Dec 2 '16 at 13:43
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    $\begingroup$ @quid chill dude, i was ASKING. $\endgroup$ – The Count Dec 2 '16 at 14:50
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    $\begingroup$ This is an exercise in the TeXbook. It’s a shame nobody reads it anymore. $\endgroup$ – Emil Jeřábek supports Monica Dec 5 '16 at 16:57
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    $\begingroup$ It’s exercise 18.14, and I have it on page 171 (this may depend on the edition). But to be fair, now I see that it is marked with a double dangerous bend. $\endgroup$ – Emil Jeřábek supports Monica Dec 5 '16 at 17:07
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    $\begingroup$ Should we perhaps start calling these Freedom Intervals? :-P $\endgroup$ – Asaf Karagila Dec 6 '16 at 16:42
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    $\begingroup$ There is already a question about this on TeX.SE: tex.stackexchange.com/questions/326237/… $\endgroup$ – Hans Lundmark Dec 6 '16 at 19:44
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    $\begingroup$ It should be noted that Don Knuth doesn't spare us his opinion either in that exercise: Some perverse mathematicians use brackets backwards, to denote “open intervals.” :-) $\endgroup$ – The Vee Dec 6 '16 at 20:23
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    $\begingroup$ Point taken, @quid. Admittedly I exaggerate this (in lecture halls, and apparently consequently also here) to drive home the point that the students should not expect their high school math books to be an ultimate authority. Particularly on conventions such as notation (or whether $0$ is a natural number or not). The "ugly" comes when yours truly handwrites things like $]1,2[\cup]3,4]$ when horizontal line segments of the brackets gain extra length. $\endgroup$ – Jyrki Lahtonen Dec 8 '16 at 7:20
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    $\begingroup$ @JyrkiLahtonen I certainly agree it is important to high-light that there are various competing and contradictory conventions. Given my shaky hand-writing, I personally am more concerned that $]$ and $)$ could morph into one another. $\endgroup$ – quid Dec 8 '16 at 16:41
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Since my comment under the other answer got about three times more votes than the answer, maybe it's worth converting it into a full answer:

The correct way would be, as far as I can tell, to convert the brackets into opening and closing delimiters through the use of \mathopen and \mathclose:

\forall x \in \mathopen{]} -1, 1 \mathclose{[}, f(x) > 0

$$\forall x \in \mathopen{]} -1, 1 \mathclose{[}, f(x) > 0$$

Compared to \left and \right, this does not scale the delimiters (which may become too big), and the spacing is slightly different (at least in LaTeX, I don't know about MathJax precisely). See What is the correct way to do delimiters? and Spacing around \left and \right at TeX.SE.

Though to be honest I'm French and was taught the French notation since (the equivalent of) sixth grade, and I don't think I've ever used it on this website, just like I don't put spaces before exclamation/interrogation marks when I write in English (even though I do prefer the French notation: is $(0,1)$ a pair or an interval?).

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    $\begingroup$ It's obviously the greatest common divisor of $0$ and $1$. $\endgroup$ – Daniel Fischer Dec 6 '16 at 10:14
  • $\begingroup$ The meaning of $(0,1)$ is always clear from the context. $\endgroup$ – MathematicsStudent1122 Dec 6 '16 at 13:06
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    $\begingroup$ @MathematicsStudent1122 that's obviously an exaggeration. Maybe 'usually' or 'most of the time' instead of 'always' would be more sensible. $\endgroup$ – quid Dec 6 '16 at 14:53
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    $\begingroup$ @quid Prove me wrong by finding a counterexample. $\endgroup$ – MathematicsStudent1122 Dec 6 '16 at 14:58
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    $\begingroup$ @MathematicsStudent1122 'clear' not being an objective notion, you could always maintain it is clear. Thus giving particular examples here is an exercise in futility. I know for a fact that I get asked questions for clarification what is meant by $(a,b)$ sometimes, some of which I would not get when it'd say $(a,b)$ or $]a,b[$ or $\gcd(a,b)$ or $\langle a, b \rangle$ depending on whether it's the couple, the open interval, the gcd or the ideal generated. // Separately, the notation with the inverted brackets is arguably also somewhat more intuitive re what is open and what is closed. $\endgroup$ – quid Dec 6 '16 at 16:28
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    $\begingroup$ @MathematicsStudent1122 Perhaps, but I prefer a notation where you don't even need the context. I don't think it's necessary to continue this argument. $\endgroup$ – Najib Idrissi Dec 6 '16 at 16:43
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Plain $\mathrm{\TeX}$ defines

\mathcode`\[="405B
\mathcode`\]="505D

\delcode`\[="05B302
\delcode`\]="05D303

and $\mathrm{\LaTeX}$ does essentially the same. One could get extensible French brackets by something like

\def\lfb{\delimiter"405D303 }
\def\rfb{\delimiter"505B302 }

Compiling the following file

\def\lfb{\delimiter"405D303 }
\def\rfb{\delimiter"505B302 }

$$
\lfb 0,1\rfb\cup \lfb 2,3\rfb
$$

$$
\left\lfb {1\over2},3\right\rfb
$$

\bye

with plain $\mathrm{\TeX}$ produces

enter image description here

with the correct spacing and extensible brackets. Also \bigl\lfb and similar commands would work.

However, MathJax doesn't understand this syntax, for obvious reasons, so it should be a feature request for them. On the other hand, simply typing

\bigl]0,1\bigr[ \cup \bigl]2,3\bigr[

produces $\bigl]0,1\bigr[\cup\bigl]2,3\bigr[$, which might be deemed sufficient. For normal sized delimiters, I see no other choice than

\mathopen]0,1\mathclose[ \cup \mathopen]2,3\mathclose[

that produces $\mathopen]0,1\mathclose[ \cup \mathopen]2,3\mathclose[$.

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  • $\begingroup$ I'm sorry, but what's the point of this answer? The whole discussion about latex is irrelevant, and your conclusion is the same as my answer no? $\endgroup$ – Najib Idrissi Dec 11 '16 at 7:42
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    $\begingroup$ @NajibIdrissi Two points: first, showing what's behind the scenes in TeX; second, that one needs a fearure request to the MathJax people. $\endgroup$ – egreg Dec 11 '16 at 9:25
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The problem with (2) is that the $\in$ sign is inside the interval. Hence we can wrap the brackets in a \newcommand:

\newcommand{\ointerv}[1]{\left] #1 \right[}

which generates

$$\newcommand{\ointerv}[1]{\left] #1 \right[} \forall x \in \ointerv{-1,1} $$

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    $\begingroup$ \left and \right will scale the brackets, which may be undesirable. The correct way in LaTeX (and, I guess, MathJax) would be \mathopen and \mathclose: $\forall x \in \mathopen{]} -1, 1 \mathclose{[}$. $\endgroup$ – Najib Idrissi Dec 2 '16 at 9:56
  • $\begingroup$ @NajibIdrissi: Why should scaling be undesirable? As I understand, \left and \right are the correct, semantic way to do things... $\endgroup$ – darij grinberg Dec 5 '16 at 22:01
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    $\begingroup$ @darijgrinberg tex.stackexchange.com/q/1454/14965 $\endgroup$ – Najib Idrissi Dec 6 '16 at 7:04
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Here's an idea: try

\newcommand{\]}{{]}}
\newcommand{\[}{{[}\,}

With that, coding \]0,+\infty\[ yields $$ \newcommand{\]}{{]}} \newcommand{\[}{{[}\,} \forall x \in \]0,+\infty\[, \quad f(x) > 0 $$

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    $\begingroup$ \[ and \] is a standard delimiter for displayed equations in MathJax (granted it's hardly used on this site as one would have to escape the characters due to interactions wit Markdown, but it does work even here), and the standard delimiter for this in LaTeX. I do not think it's a good idea to use this particular syntax, but it'd be easy to rename it. $\endgroup$ – quid Dec 2 '16 at 9:29
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    $\begingroup$ Wow, that seems obvious in retrospect $\endgroup$ – Omnomnomnom Dec 2 '16 at 13:43
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    $\begingroup$ Still a good answer I think, but the macros would maybe need to be renamed. $\endgroup$ – 6005 Dec 2 '16 at 22:30

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