# Symbols:General

## Symbols for General Use

### 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.

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}.