[Tex/LaTex] About the use of curly braces

math-modemath-operatorssyntax

Although I use LaTeX a lot, I still have a lot to learn about it, and I still have many questions which remain unanswered. One in particular bothers me: when and why must I use curly brackets when giving arguments to a function like \cos or \sin?

I tend to use curly brackets everywhere and write \cos{x}, because that's how it was written on documents I used to teach myself. However, I see a lot of LaTeX documents where the syntax is simply \cos x.

Does it have any importance? Maybe when writing a lot of these functions at a time, like r\sin \theta d\phi?

Thanks for your help!

Best Answer

Note that the braces are not just not required, they should not be used as \cos does not take an argument the braces form a group and force the term to lose any special math class that it would otherwise have.

\cos is a "\mathop" operator and ( is a "\mathopen" but a term surrounded by {..} is always a "\mathord". TeX uses different space between a \mathop and a \mathopen than between a \mathop an a \mathord (because log(x) does not need any space but log x does).

Compare

\documentclass{article}

\begin{document}

$\cos(\phi+\theta)$

$\cos{(\phi+\theta)}$

\end{document}

which produces

Related Solutions

[Tex/LaTex] Curly braces in math mode

Use \{…\}. But, as the contents inside the braces may vary in size, it would be better to use the DeclarePairedDelimiter command from the mathtools package:

\DeclarePairedDelimiter\set\{\}

This defines a \set{…} command, which accepts an optional argument: \big, \Big, \bigg, or \Bigg, which implicitly adds a pair of \bigl…\bigr, &c. in front of the braces. Example: \set[\big]{...}

A \set*{…} variant becomes available for free, which adds implicitly a pair of \left…\right.

[Tex/LaTex] Creating curly braces with limits

For me the standard way works. Have you tried this?

\documentclass[]{article}

\usepackage{amsmath}

\begin{document}
Thus, we get
\[
  \bigl\{\beta^w_{u_j}\bigr\}_{j=1}^n
\]
and
\[
  \bigl\{\beta^m_{u_j}\bigr\}_{j=1}^n
\]

In the same line:
\[
  \bigl\{\beta^w_{u_j}\bigr\}_{j=1}^n
  \quad\text{and}\quad
  \bigl\{\beta^m_{u_j}\bigr\}_{j=1}^n
\]

This is a long line, so that the equations are in the middle of two lines.
Everything in the same line using inline $\bigl\{\beta^w_{u_j}\bigr\}_{j=1}^n$
and $\bigl\{\beta^m_{u_j}\bigr\}_{j=1}^n$. But this doesn't look good, because
it might stretch the linespacing.

Using 
\[
  \text{Thus, we get}\quad%
  \bigl\{\beta^w_{u_j}\bigr\}_{j=1}^n
  \quad\text{and}\quad
  \bigl\{\beta^m_{u_j}\bigr\}_{j=1}^n
\]
does look better for the line spacing, but honestly it is not that pretty, imho.
\end{document}

Best Answer

Related Solutions

[Tex/LaTex] Curly braces in math mode

[Tex/LaTex] Creating curly braces with limits

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