Symbols:General

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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}.