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.