# Symbols of height intermediate between \big and \Big needed

I consistently find that math symbols scaled with \big/\bigl/\bigr are too small and those scaled with \Big/\Bigl/\Bigr are too tall. Here is an example:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

$$\lvert x^2 + y^2 \rvert$$
$$\bigl\lvert x^2 + y^2 \bigr\rvert$$
$$\Bigl\lvert x^2 + y^2 \Bigr\rvert$$

$$\bigl\{ \bigl\lvert x^2 + y^2 \bigr\rvert \mathrel{\big|} 5|x \wedge 7|y \bigr\}$$
$$\Bigl\{ \bigl\lvert x^2 + y^2 \bigr\rvert \mathrel{\Big|} 5|x \wedge 7|y \Bigr\}$$

$$a/b \big/ c/d \Big/ e/f \big/ g/h$$

\end{document}


In the first line, the middle/right formulas were created with \big and \Big, respectively. In the second line, the left-hand set uses \big for the set delimiters and its middle, and the right-hand set uses \Big for them. I want something larger than \big but not as huge as \Big.

I'm not really asking anyone to fix this for me, which I suspect would be a nontrivial task. I am inquiring about the infrastructure for this and any possible future extensions.

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In my opinion you need no \big in the set description; rather you want to use : instead of \mid, if the bar for the absolute value frequently appears at its side. –  egreg Jan 1 at 21:56
@egreg Typographically you are right about the middle delimiter. (I guess I'm used to |. Though a case for consistency within a document can arise, and perhaps changing everything to : might look bad for other reasons.) –  Lover of Structure Jan 1 at 22:07

You need no \bigX for the absolute value, the output of

\lvert x^{3}+y^{3}\rvert


is just right. The same would be for parenthesized expressions, such as

(x+y)(x-y)(x^{2}+y^{2})=x^{4}+y^{4}


where \bigX for the last factor would be even wrong: compare the results, in the second line I used \bigl(x^{2}+y^{2}\bigr)

I have no doubt whatsoever that the top one is right and the bottom one is wrong.

Similarly, for your set description I'd use no \bigX command. I'd probably adjust my notation if bars for the absolute value and divisibility appear often in set descriptions, preferring the colon.

\{\, \lvert x^{3}+y^{3}\rvert : 5\mid x \land 7\mid y\,\}


or, if you want to stick with the bar, I'd increase the braces and only the separating bar:

\bigl\{\, \lvert x^{3}+y^{3}\rvert \bigm| 5\mid x \land 7\mid y\,\bigr\}


(of course, in any case I'd define a macro for this)

Double parentheses rarely need to be increased in size:

2(x-(x+y))=2(x-x-y)=-2y


produces

which is correct, while the \bigX version wouldn't be:

You're adding nothing to clarity and, instead, much to complicatedness. I'm not saying \bigl and \bigr should never be used; but not in simple cases like these. Reserve them when really an ambiguity could arise.

Your last expression is something that should never appear in mathematics. Never ever. No typographical device can make it understandable. I call them “eight story expressions”: middle school books are full of that stuff, which has the only effect of making math looking absurd. No good teacher would want it. Bad teachers unfortunately exist, they use “eight story expressions” and they won't listen to advice. :-(

One last note: there are \bigm, \Bigm, \biggm and \Biggm that make a binary relation symbol with the following delimiter.

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My examples were for demonstrative purposes; I wouldn't normally write my third line/example either, and normally using \left and \right ought to work. So, in this case I am (somewhat less absolutely) with you in your aesthetic opinion, in that the existing options are okay. Your answer is appreciated as information. That said, I think my formulas demonstrate a (discrete! ☺) discontinuity in scaling. I'm wondering what in LaTeX's infrastructure would need to be amended to fill in an additional size, or whether some LuaTeX module can easily address it etc. –  Lover of Structure Jan 4 at 2:48
I think you have a tendency to interpret questions as X-Y problems. (Typographically, I tend to agree with a decent proportion of your opinion.) In my case, I'm often trying to find examples for abstract questions, which may or may not be ideal and may or may not have other solutions. For many of my questions it's that my examples are attempts at illustrating an abstract question, not that my abstract question grew out of the specific toy example I'm showing. Often there was larger context not worth embedding into a TeX.SX question. –  Lover of Structure Jan 4 at 3:05
@LoverofStructure The scaling is discontinuous because each size needs a different glyph. With OpenType fonts it may be possible to have more than a few sizes; or you should create a new font containing math parentheses at whatever sizes you need. –  egreg Jan 4 at 10:01
It's obvious that the scaling is discrete, and it is indeed not clear that it would be beneficial to have continuous scaling. Obviously the above is a discrete discontinuity, a jump between sizes where – if considered in isolation – the \big-sizes seem typographically too small and the \Big-sizes seem too large. I also don't think that creating a new font is necessary; I have a feeling that sufficiently simple ad-hoc sizing can be done with scalerel. –  Lover of Structure Jan 29 at 11:14