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}
.