# Brackets after \qquad {}

Regarding your first question: In general it is necessary to follow this advice and simulate the first operand by `{}`

, to allow TeX to distinguish between unary and binary operators. It is just that the `align`

environment treats operators differently; `\qquad`

does not simulate an operand. So if you don't know otherwise, I'd follow the advice.

The following document demonstrates the effect (or non-effect) of a pair of braces.

```
\documentclass{article}
\usepackage[fleqn]{amsmath}
\begin{document}
$+10x$
${}+10x$
$\qquad+10x$
$\qquad{}+10x$
\begin{align*}
&+10x\\
&{}+10x\\
&\qquad+10x\\
&\qquad{}+10x
\end{align*}
\end{document}
```

Your source is incorrect, but the additional `{}`

doesn't hurt.

Let me explain what happens. The `align`

environment builds pairs of aligned columns, with cells in math mode that are right aligned in the odd-numbered columns and left aligned in the even-numbered ones.

Each cell in an even-numbered cell begins with an implicit `{}`

, which makes for an empty Ord atom.

The processing of math mode material is quite complex, but not really too complicated.

Each item can be a math atom or “other”; spacing commands are in the “other” category. Subscripts and superscripts are attached to the math atom they belong to, so they are not of a concern here. Math atoms can be of several types:

- Ord (ordinary symbol)
- Op (operator)
- Bin (binary operation symbol)
- Rel (relation symbol)
- Punct (punctuation symbol)
- Open (opening delimiter)
- Close (closing delimiter)

and some others that, however, are basically transformed into Ord; in order to keep it simple, I'll not analyze them.

The formula TeX finds when processing the `& \qquad + 10x`

line is

```
{} \qquad + 1 0 x
```

(because `&`

implies it belongs in an even-numbered column) that translates in the following sequence of atoms and other items (denoted by “X”)

Ord X Bin Ord Ord Ord

The sequence of math atoms determines the spacings that are automatically added. If a Bin atom is preceded and followed by Ord atoms, TeX inserts around it a medium space, *independently* of “other items” in between; no space is inserted between Ord atoms. You find the complete list at https://tex.stackexchange.com/a/240579/4427

After automatically inserted spaces are dealt with, TeX builds a horizontal box with the items, this time keeping into account the “other items”, so you get

(empty)

`\qquad`

(medium space)`+`

(medium space)`1`

`0`

`x`

(the spaces above are just for separating items)

If the line had been `& \qquad {} + 10x`

, the formula would become `{} \qquad {} + 10x`

and the sequence of atoms and other items would be

Ord X Ord Bin Ord Ord Ord

that would add spaces so to get

(empty)

`\qquad`

(empty) (medium space)`+`

`1`

`0`

`x`

and the result would be the same, because an empty atom produces nothing (apart possibly from triggering an automatic insertion of spaces).

This has been the behavior of `amsmath`

since its release, even when it was called `amslatex`

, so 1992 or so.

The purpose of the implicity empty Ord atom is to get correct spacing in a typical `align`

:

```
\begin{align}
A &= B+C \\
D &= E+F
\end{align}
```

where `B+C`

is not really typical, but is used by way of example. The sequence of atoms when processing the second cell in the first row would come from

```
{} = B + C
```

so translated into

Ord Rel Ord Bin Ord

and, since TeX inserts a thick space between either Ord-Rel or Rel-Ord, we get

(empty) (thick space)

`=`

`B`

(medium space)`+`

(medium space)`C`

This is to allow the result to be the same as if it had been `A=B+C`

as far as automatically inserted spacing is concerned.

Actually, there *is* a place where to be careful: if a cell in an even-numbered column starts with an `Op`

atom (such as `\sum`

or `\log`

), a thin space would be inserted, because TeX automatically adds it between Ord and Op.

Is there a difference between `\qquad{}`

and `\qquad {}`

? No. Spaces after a control word are ignored.