Symbols:General/Ellipsis

From ProofWiki
Jump to: navigation, search

Ellipsis

$\ldots$ or $\cdots$

An ellipsis is used to indicate that there are omitted elements in a set or a sequence whose presence need to be inferred by the reader.

For example:

$1, 2, \ldots, 10$

is to be understood as meaning:

$1, 2, 3, 4, 5, 6, 7, 8, 9, 10$


There are two forms of the horizontal ellipsis, one on the writing line which is to be used for punctuation separated lists:

$a, b, \ldots, z$

and one centrally placed in the line, to be used in other circumstances, for example, in expressions assembled using arithmetic operations:

$a + b + \cdots + k$

There also exist vertically and diagonally arranged ellipses, for use in the structure of matrices:

$\begin{array}{c} a \\ \vdots \\ b \end{array} \qquad \begin{array}{c} a \\ & \ddots \\ & & b \end{array}$


The $\LaTeX$ code for \(1, 2, \ldots, 10\) is 1, 2, \ldots, 10 .

The $\LaTeX$ code for \(1 + 2 + \cdots + 10\) is 1 + 2 + \cdots + 10 .

The $\LaTeX$ code for \(\vdots\) is \vdots .

The $\LaTeX$ code for \(\ddots\) is \ddots .


Linguistic Note

The plural of ellipsis is ellipses.

This is pronounced ell-ip-seez, where the final syllable is long.


Do not confuse with the plural of ellipse, which is spelt the same but is pronounced ell-ip-siz.


Also see