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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`

¶Ellipsis on the baseline, …. Used as:

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

. Another example is the above array example. A synonym is`\mathellipsis`

. 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`

. (In a paragraph mode or LR mode a synonym for`\ldots`

is`\dots`

.)`\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.