Ellipses are the three dots (usually three) indicating that a pattern continues.

\begin{array}{cccc} a_{0,0} &a_{0,1} &a_{0,2} &\ldots \\ a_{1,0} &\ddots \\ \vdots \end{array}

LaTeX provides these.

`\cdots`

¶Horizontal ellipsis with the dots raised to the center of the line, as in ⋯. Used as:

`\( a_0\cdot a_1\cdots a_{n-1} \)`

.`\ddots`

¶Diagonal ellipsis, ⋱. See the above array example for a usage.

`\ldots`

¶`\mathellipsis`

¶`\dots`

¶Ellipsis on the baseline, …. Used as:

`\( x_0,\ldots x_{n-1} \)`

. Another example is the above array example. Synonyms are`\mathellipsis`

and`\dots`

. A synonym from the`amsmath`

package is`\hdots`

.You can also use this command outside of mathematical text, as in

`The gears, brakes, \ldots{} are all broken`

.`\vdots`

¶Vertical ellipsis, ⋮. See the above array example for a usage.

The `amsmath`

package has the command `\dots`

to semantically
mark up ellipses. This example produces two different-looking outputs
for the first two uses of the `\dots`

command.

\usepackage{amsmath} % in preamble ... Suppose that \( p_0, p_1, \dots, p_{n-1} \) lists all of the primes. Observe that \( p_0\cdot p_1 \dots \cdot p_{n-1} +1 \) is not a multiple of any \( p_i \). Conclusion: there are infinitely many primes \( p_0, p_1, \dotsc \).

In the first line LaTeX looks to the comma following `\dots`

to
determine that it should output an ellipsis on the baseline. The second
line has a `\cdot`

following `\dots`

so LaTeX outputs an
ellipsis that is on the math axis, vertically centered. However, the
third usage has no follow-on character so you have to tell LaTeX what
to do. You can use one of the commands: `\dotsc`

if you need the
ellipsis appropriate for a comma following, `\dotsb`

if you need
the ellipses that fits when the dots are followed by a binary operator
or relation symbol, `\dotsi`

for dots with integrals, or
`\dotso`

for others.

The `\dots`

command from `amsmath`

differs from the
LaTeX kernel’s `\dots`

command in another way: it outputs a
thin space after the ellipsis. Furthermore, the `unicode-math`

package automatically loads `amsmath`

, so `amsmath`

’s
`\dots`

may be active even when you did not explicitly load it,
thus changing the output from `\dots`

in both text and math mode.

Yet more about the ellipsis commands: when running under Unicode
engines (`lualatex`

, `xelatex`

), LaTeX will use the
Unicode ellipsis character (U+2026) in the font if it’s available;
under traditional TeX engines (`pdflatex`

, `latex`

), it
will typeset three spaced periods. Generally, the Unicode
single-character ellipsis has almost no space between the three
periods, while the spacing of the non-Unicode ellipsis is looser, more
in accordance with traditional typography.