Is it ever bad to use \left and \right?

Question

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!

Answer 1

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.

Answer 2

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 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. They 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.\ $\bigl((a+b)(c+d)\bigr)$
  

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

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

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 mean to single out any one person in particular):

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.

Answer 3

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}

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.}

Another example, where the box is artificially spread out in order to emulate a line of type where interword spaces are enlarged for justification:

\documentclass{article}

\begin{document}

Not too much spread:

\makebox[\dimexpr\width+1pc][s]{Text $y-y_0=m\left(x-x_0\right)$ and other text}

\makebox[\dimexpr\width+1pc][s]{Text $y-y_0=m(x-x_0)$ and other text}

\medskip

Larger spread:

\makebox[\dimexpr\width+2pc][s]{Text $y-y_0=m\left(x-x_0\right)$ and other text}

\makebox[\dimexpr\width+2pc][s]{Text $y-y_0=m(x-x_0)$ and other text}

\end{document}

The lines with \left and \right are wider because of the added space around \left and \right; in those lines the spaces around the minus sign in x-x_0 don't stretch, because \left(...\right) makes a subformula with rigid spaces. The effect is more evident in the second pair of lines. Note that the delimiters are not bigger (and they shouldn't be anyway, in this case).

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 hung on museums' walls, but read by people: the fewer distractions, the easier will be reading it.

Answer 4

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}

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.