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For mathematics, is it ever disadvantageous to use \left( and \right) in equations?

I can't see any way that doing this would hinder the typesetting, so why isn't () just converted into \left( \right) automatically? This would save a lot of typing.

Cheers!

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marked as duplicate by Ingo, Jesse, Thorsten, Malipivo, ChrisS Apr 30 at 10:06

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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Welcome to TeX.SX!] A tip: You can use backticks ` to mark your inline code as I did in my edit. –  Adam Liter Apr 27 at 3:29
    
@AdamLiter I see, thank you. –  user50612 Apr 27 at 3:30
    
See Macro for \left( and \right) –  A.Ellett Apr 27 at 3:32
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For mathematics... no. For typography, maybe; I'm sure some like it, while other go without it happily. –  Werner Apr 27 at 4:59

4 Answers 4

up vote 34 down vote accepted

The automatic sized braces are not always the sizes you would choose manually, but that's a matter of personal taste (and the sizes chosen by the automatic algorithm can be adjusted with the \delimitershortfall and \delimiterfactor parameters).

More immediate problems are that \left( ... \right) differs from ( ... ) even if the standard small delimiter size is chosen.

  • It is a \mathinner atom so it gets additional spacing in many contexts.

  • It is a \mathinner atom so can not be broken across lines in a math display such as align.

  • It is a \mathinner atom so will not allow automatic linebreaking in inline math.

  • It is a \mathinner atom so forms a box set to its natural length and white space around relations or added explicitly will not be allowed to stretch or shrink to help with line breaking.

  • It is a \mathinner atom.

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2  
Your bullets all say "it", but it's not clear to me whether your pronoun is referencing \left( ... \right( or ( ... ), or something else (singular), since they are plural. –  Travis Bemrose Apr 27 at 15:51
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@TravisBemrose the construct \left( stuff \right) makes a single math atom in the same way that \mbox{ stuff} makes a single box. –  David Carlisle Apr 27 at 15:56
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whoever downvoted this, why?? I can understand vim users downvoting my emacs answers, but I'm a bit bemused by this one. –  David Carlisle May 11 at 22:16

You ask:

For [mathematical typography], is it ever disadvantageous to use \left( and \right) in equations?

Excerpting from pp. 148f. of the TeXbook (emphasis added):

At this point you are probably wondering why you should bother learning about \bigl and \bigr and their relatives, when \left and \right are there to calculate sizes for you automatically. Well, it's true that \left and \right are quite handy, but there are at least three situations in which you will want to use your own wisdom when selecting the proper delimiter size: (1) Sometimes \left and \right choose a smaller delimiter size than you want. [...] (2) Sometimes \left and \right choose a larger delimiter than you want. [...] (3) Sometimes you need to break a huge displayed formula into two or more lines, and you want to make sure that that its opening and closing delimiters have the same size; but you can't use \left on the first line and \right on the last, since \left and \right must occur in pairs. [...]

To illustrate the first two cases, consider the following two examples that contrast indiscriminate use of \left and \right with judicious use of \big and \bigg.

  • Here's a case where \left( ... \right) produce parentheses that aren't big enough:

    $\left(\left(a+b\right) \left(c+d\right)\right)$ vs.\ $\bigl((a+b)(c+d)\bigr)$
    

enter image description here

  • And here's a case where \left( ... \right) produce parentheses that are too big from a typographic point of view:

    $\displaystyle\left(\sum_{i=1}^\infty\frac{1}{i^2}\right)^2 \mbox{ vs.\ } 
     \biggl(\,\sum_{i=1}^\infty\frac{1}{i^2}\biggr)^{\!2}$
    

enter image description here

Note that the second expression not only employs \biggl( and \biggr) but also uses a positive thinspace after the opening parenthesis and a negative thinspace to position the exponent 2. Incidentally, the recommendation to use \biggl( and \biggr) in this case instead of \left( and \right) isn't just my personal preference; it's also given on p. 149 of the TeXbook.

  • Even if the size of the parentheses produced by \left( ... \right) happens to be correct, the spacing around the large parentheses may not only be suboptimal from a purely typographic/aesthetic point of view but actually interfere with the normal interpretation of some standard operators. Consider, for instance, the following expression (culled from a recent posting to this site; I won't say which posting as I don't single out any one person in particular):

enter image description here

In the first row, \left and \right are used to size the square brackets. Because \left[ inserts a bit of extra whitespace to its immediate left, the enlarged space after \pm makes it look like it might be a binary operator; the reader may thus be puzzled by how one is supposed to add a \sum symbol and a term in square brackets -- before concluding that \pm is a unary operator and that what the author intended to say is that the sum is taken over the positive and negative values of the term in square brackets... By using \bigl[ (see the look in the second row), such ambiguity doesn't arise to begin with.


There are still further reasons for not using \left and \right indiscriminately. See, e.g., the answer by David Carlisle for reasons related to (i) a lack of intelligent spacing inside a \left...\right pair and (ii) inability to let TeX find a line break within a \left...\right pair that's used in inline math mode.

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Your ((a+b)(c+d)) is the first example I've seen where \left( ... \right) didn't chose the sizing I'd want it to. Even in the second example, I prefer it over \biggl( ... \bigr) because they leave the i=1 hanging out, making it look like it's not part of the expression, or like it may "fall away". –  Travis Bemrose Apr 27 at 16:09
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@TravisBemrose - Good typography is characterized by balance, meaning that no one element dominates the others. Whereas the \left(...\right) approach does ensure that the material is fully enclosed, the resulting very large parentheses tend to dominate the enclosed material. The \biggl(...\biggr) approach tries to strike a balance: both the parentheses and the material they enclose are given roughly equal visual importance. And do ask yourself: what's the risk that a reader might think that "i=1" isn't part of the expression, just because it's not "fully enclosed" by the parentheses? –  Mico Apr 27 at 17:00
    
Yes, larger has drawbacks. On your last point, I wasn't trying to imply that it wouldn't be clear or the reader wouldn't understand. I was indicating that the part of my brain that deals with a physical 3D world, distracts the part of my brain that deals with abstract equations. I can read the first faster. Internal conflict or at least multi-tasking slows down my ability to process the second. Not to a snails pace certainly, but "slightly longer" when you're talking about sub-second timing can mean ~1.5 - 3 times longer. –  Travis Bemrose Apr 27 at 17:11

Here's an example: in the first display, \left and \right are used throughout, while in the second several manual adjustments have been made in order to properly typeset the formulas.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
\lim_{t\to\infty}\left(1+\frac{r}{t}\right)^{tn}=
\lim_{t\to\infty}\left(\left(1+\frac{r}{t}\right)^{t}\right)^{n}=
\left(\lim_{t\to\infty}\left(1+\frac{r}{t}\right)^{t}\right)^{n}=
\left(e^{r}\right)^{n}=
e^{rn}
\]
\[
\lim_{t\to\infty}\Bigl(1+\frac{r}{t}\Bigr)^{\!tn}=
\lim_{t\to\infty}\Bigl(\!\Bigl(1+\frac{r}{t}\Bigr)^{\!t\,}\Bigr)^{\!n}=
\Bigl(\,\lim_{t\to\infty}\Bigl(1+\frac{r}{t}\Bigr)^{\!t\,}\Bigr)^{\!n}=(e^r)^n=
e^{rn}
\]
\end{document}

enter image description here

I have no doubt whatsoever that the second version is better: it's more readable and less distracting. Yes, it requires some labor, but let me remind what τέχνη (techne) means:

τέχν-η , ἡ, (τέκτων)
A. art, skill, cunning of hand, esp. in metalworking, Od.3.433, 6.234, 11.614; also of a shipwright, Il.3.61; of a soothsayer, A.Ag.249 (pl., lyr.), Eu.17, S.OT389, etc.; “τέχναι ἑτέρων ἕτεραι” Pi.N.1.25; “ὤπασε τ. πᾶσαν” Id.O.7.50.
2​. craft, cunning, in bad sense, δολίη τ. Od.4.455, Hes.Th.160: pl., arts, wiles, Od.8.327.332, Hes.Th.496,929; “δολίαις τέχναισι χρησάμενος” Pi.N.4.58; τέχναις τινός by his arts (or simply by his agency), Id.O.9.52, P.3.11; τέχνην κακὴν ἔχει he has a bad trick, Hes.Th.770, cf. Pi.I.4(3).35(53), S Ph.88, etc.
3​. way, manner, or means whereby a thing is gained, without any definite sense of art or craft, μηδεμιῇ τ. in no wise, Hdt.1.112; ἰθέῃ τ. straightway, Id.9.57; πάσῃ τ. by all means, Ar.Nu.1323, Th.65, Ec.366; παντοίᾳ τ. S.Aj.752, etc.; “οὐκ ἀποστήσομαι . . οὔτε τ. οὔτε μηχανῇ οὐδεμιᾷ” IG12.39.22; “πάσῃ τ. καὶ μηχανῇ” X.An.4.5.16; “μήτε τ. μήτε μηχανῇ μηδεμιᾷ” Lys.13.95.

[…]

Henry George Liddell. Robert Scott. A Greek-English Lexicon. revised and augmented throughout by. Sir Henry Stuart Jones. with the assistance of. Roderick McKenzie. Oxford. Clarendon Press. 1940.

Typography is not just laying down letters, but it's also a craft and, in some cases (not this one, of course), art. As such we can't think that any automated system will be able to avoid human judgment.

TeX allows automation, with a not so bad output; if we want our documents to be good, we have to work on them. A good document is not to be hanged on museums' walls, but read by people: the less distractions, the easier will be reading it.

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+1 for "As such we can't think that any automated system will be able to avoid human judgment". –  Papiro Apr 27 at 12:57
    
I find the 2nd one to be distracting, and much prefer the first. –  Travis Bemrose Apr 27 at 15:58
    
@TravisBemrose Yes that's interesting... I also prefer the first. I find it helpful when the outer parentheses are larger than the inner ones so that nesting is clear. –  user50612 Apr 27 at 16:00
    
@TravisBemrose Everybody is entitled their own opinions. :-) Increasing the size of the parentheses places superscripts in almost random positions, while they are conceptually at the same level: $(a^{x})^{y}=a^{xy}$ –  egreg Apr 27 at 16:00
    
Yes. :-) I take your point that conceptually they are at the same level, but they're not being applied the same. If there's a reason to use parentheses to place them at different levels (as in the example), I find it a mental assist to emphasize the separation of the operations. It also helps me pair-match quickly, when each pair is a different size. And lastly, I find the way the t exponent sticks out of the outer parenthesis unaesthetic. (And the way the inner t hangs out of the bottom of its own parentheses, but that's not worth the effort, so I breathe and move on.) –  Travis Bemrose Apr 27 at 16:18

There are many reasons. The simplest one is of an aesthetic nature (edited according to some suggestions from the comments):

\documentclass{article}

\begin{document}

Is:
\[
\left(\sum_{n=1}^\infty\frac1{n^2}\right)^2=\frac{\pi^4}{36}
\]
Should be:
\[
\Bigl(\sum_{n=1}^\infty\frac1{n^2}\Bigr)^2=\frac{\pi^4}{36}
\]
or 
\[
\biggl(\sum_{n=1}^\infty\frac1{n^2}\biggr)^2=\frac{\pi^4}{36}
\]
(with some addidional corrections  after the opening parenthesis).

\end{document}

enter image description here

The braces choosen in the first example are too big and should be corrected.

If an equation is splitted into many lines, there are no matching \left or \right.

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15  
I actually think the first example looks nicer, because it contains the whole summation... –  user50612 Apr 27 at 3:41
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@user50612 But one of typographic rules (I am not sure, if in all countries) says, that the braces should be approximately as big as the summation sign (here), but without its limits. –  Przemysław Scherwentke Apr 27 at 3:47
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@PrzemysławScherwentke, That's not universal, at least. Swedish Almqvist & Wiksells sättningsregler (Lansburgh 1961, p. 261) would prefer the first example (but smaller parens if there would have been only a subscript, but no superscript to the summation symbol). –  pst Apr 27 at 4:45
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I'd use \biggl and \biggr in that case; with \Bigl the parenthesis is too short (a \, after the opening parenthesis could improve). For the exponent, ^{\!2} is recommended, in order to compensate for the curved shape of the closing parenthesis. –  egreg Apr 27 at 9:46
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@pst - Believe it or not, but not everyone has easy access to a copy of Lansburgh (1961). Is it available online somewhere? –  Mico Apr 27 at 11:28

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