Editing Ellipsis (section)

==In mathematical notation==
An ellipsis is used in [[mathematics]] to mean "and so forth"; usually indicating the omission of terms that follow an obvious pattern as indicated by included terms.

The whole numbers from 1 to 100 can be shown as:

: <math>1,2,3,\ldots,100</math>

The positive whole numbers, an infinite list, can be shown as:

: <math>1,2,3,\ldots</math>

To indicate omitted terms in a repeated operation, an ellipsis is sometimes raised from the baseline, as:<ref name="MerriamWebster" />{{rp|115}}

: <math>1+2+3+\cdots+100</math>

But, this raised formatting is not standard. For example, Russian mathematical texts use the baseline format.<ref>Мильчин А. Э. [http://slovari.yandex.ru/~книги/Издательский%20словарь/Многоточие%20в%20математических%20формулах/ Издательский словарь-справочник] {{Webarchive|url=https://web.archive.org/web/20150326175211/https://slovari.yandex.ru/~%D0%BA%D0%BD%D0%B8%D0%B3%D0%B8/%D0%98%D0%B7%D0%B4%D0%B0%D1%82%D0%B5%D0%BB%D1%8C%D1%81%D0%BA%D0%B8%D0%B9%20%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D1%80%D1%8C/%D0%9C%D0%BD%D0%BE%D0%B3%D0%BE%D1%82%D0%BE%D1%87%D0%B8%D0%B5%20%D0%B2%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D1%85%20%D1%84%D0%BE%D1%80%D0%BC%D1%83%D0%BB%D0%B0%D1%85/ |date=2015-03-26 }}.— Изд. 3-е, испр. и доп., Электронное — М.: ОЛМА-Пресс, 2006. (in Russian)</ref>

The ellipsis is not a formally defined [[mathematical symbol]]. Repeated summations or products may be more formally denoted using [[Capital sigma notation|capital sigma]] and [[capital pi notation]], respectively:

: <math>1+2+3+\cdots+100\ = \sum_{n=1}^{100} n = 100?</math> (see [[termial]])
: <math>1 \times 2 \times 3 \times \cdots \times 100\ = \prod_{n=1}^{100} n = 100!</math> (see [[factorial]])

Ellipsis is sometimes used where the pattern is not clear. For example, indicating the indefinite continuation of an [[irrational number]] such as:

: <math>\pi=3.14159265\ldots</math>

It can be useful to display an expression compactly, for example:

: <math>1+4+9+\cdots+n^2+\cdots+400</math>

In [[set notation]], the ellipsis is used as horizontal, vertical and diagonal for indicating missing [[Matrix (mathematics)|matrix]] terms, such as the size-''n'' [[identity matrix]]:

: <math>I_n = \begin{bmatrix}1 & 0 & \cdots & 0 \\0 & 1 & \cdots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \cdots & 1 \end{bmatrix}</math>