# Symbols:General

## Contents

## 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`

.

## Equals

- $x = y$ means
**$x$ is the same object as $y$**, and is read**$x$ equals $y$**, or**$x$ is equal to $y$**.

- $x \ne y$ means
**$x$ is not the same object as $y$**, and is read**$x$ is not equal to $y$**.

The expression:

- $a = b$

means:

- $a$ and $b$ are names for the same object.

The $\LaTeX$ code for \(=\) is `=`

.

The $\LaTeX$ code for \(\ne\) is `\ne`

or `\neq`

.

## Negation

- $\not=, \ \not>, \ \not<, \ \not \ge, \ \not \le, \ \not \in, \ \not \exists, \ \not \subseteq, \ \not \subset, \ \not \supseteq, \ \not \supset$

The above symbols all mean the opposite of the non struck through version of the symbol.

For example, $x \not\in S$ means that $x$ is not an element of $S$.

The slash $/$ through a symbol can be used to reverse the meaning of essentially any mathematical symbol (especially relations), although it is used most frequently with those listed above.

- Note
- Using $/$ with
`\subsetneq`

and`\supsetneq`

can be confusing:- $\not \subsetneq, \ \not \supsetneq$

- as the strike through of the symbol as a whole obscures the clarity of the strike through of the equivalence bar on the bottom, and hence should be avoided.

- The constructs
`\not \subsetneqq`

and`\not \supsetneqq`

can be used instead, but these are unwieldy and look suboptimal:- $\not \subsetneqq, \ \not \supsetneqq$

- and it is suggested that a statement that requires this concept be restructured so as to avoid such a construct.

The $\LaTeX$ code for negation is `\not`

followed by the code for whatever symbol you want to negate.

For example, `\not \in`

will render $\not \in$.

Note that several of the above relations also have their own $\LaTeX$ commands for their negations, for example `\ne`

or `\neq`

for `\not =`

, and `\notin`

for `\not \in`

.

## Prime

- $x'$

The symbol $'$ is a general indicator of **another version of** or **another type of** where the specific version or type that is being described is to be defined.

The symbol $x'$ should technically be voiced **x prime**, although colloquially referred to as some variant of **x dash** or **x tick** or whatever can be devised by the ingenuity of the reader.

The $\LaTeX$ code for \(x'\) is `x'`

or `x^{\prime}`

.