When we create mathematical expressions or formulas using LaTeX, we need different symbols. Among these, the vertical bar is a common symbol, which you will learn to use in this tutorial.

There are various commands for using the symbol, such as `|`

, `\mid`

, `\vert`

, etc. Each command has its own use and relevance. Below, we discuss with examples which command to use in which situation.

```
\documentclass{article}
\begin{document}
\[a|b\]
\[a\vert b\]
\[a\mid b\]
\end{document}
```

**Output :**

The above three are math mode commands used in `ред`

and `\vert`

for both text and equations and they don’t need any spaces on either side.

The `\mid`

command should be used when you want to indicate conditions or division, and **it automatically adds a small space on both sides**, which `|`

or `\vert`

commands do not.

## Using different sizes of vertical bars

At times, you may need to use vertical bars of different sizes. In LaTeX, you can use commands like `\big|`

, `\Big|`

, `\bigg|`

, and `\Bigg|`

to set the size of the delimiters. For example:

```
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[a \big| b \quad a \Big| b \quad a \bigg| b \quad a \Bigg| b\]
\[\cfrac{1}{x}\,\Bigg|_{a}^{b}\]
\end{document}
```

**Output :**

If you want to use the \mid command to indicate conditions or divisions within a set and show them in different sizes, you can use the commands `\bigm|`

, `\Bigm|`

, `\biggm|`

, and `\Biggm|`

. These commands work like \mid but are larger in size.

```
\documentclass{article}
\usepackage{amsmath,amsfonts}
\begin{document}
\[ a \bigm| b \qquad a \Bigm| b \qquad a \biggm| b \qquad a \Biggm| b \]
\[ \left\{ x \in \mathbb{R} \Biggm| x^2 \leq 4 \right\} \]
\end{document}
```

**Output :**

## Using \left. and \right|

With the `\left.`

and `\right|`

commands, you can add a vertical bar that automatically adjusts to the height of expression.

Here, `\left.`

is an invisible delimiter. It is used when you want a matching delimiter on the right side but do not want anything to appear on the left side.

Using `\left.`

, **you indicate to LaTeX that a delimiter starts here, but it is not visible.**

```
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[\left. \int_0^x t^2 \, dt \right|_{x=1} \]
\[\left. \cfrac{dy}{dx} \right|_{x=0} \]
\end{document}
```

**Output :**

In this example, `\left.`

creates an empty space on the left side of the expression without adding a visible bracket, and **\right| adds a vertical bar that adjusts to the height of the expression.**

## Double vertical bar symbol

In LaTeX, to create a double vertical bar symbol, you can use the `\|`

or `\Vert`

commands. But, `\Vert`

is a bit more formal and used in specific situations.

```
\documentclass{article}
\begin{document}
\[a \| b\]
\[a \Vert b\]
\end{document}
```