Symbols:Glossary
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Glossary
This page contains a glossary of symbols and terms which are often used on $\mathsf{Pr} \infty \mathsf{fWiki}$ without a direct link to a definition page.
| \(\leadsto\) | $\quad:\quad$\leadsto
|
$\qquad$see Distinction between Logical Implication and Conditional | |
| \(\leadstoandfrom\) | $\quad:\quad$\leadstoandfrom
|
$\qquad$same as $\leadsto$ but goes both ways | |
| \(:\) | $\quad:\quad$:
|
$\qquad$such that: what came before this is qualified by what comes after it | |
| \(:=\) | $\quad:\quad$:=
|
$\qquad$is defined as | |
| \(=:\) | $\quad:\quad$=:
|
$\qquad$is a definition for | |
| \(\set {\cdots}\) | $\quad:\quad$\set {\cdots}
|
$\qquad$a general set | |
| \(\in\) | $\quad:\quad$\in
|
$\qquad$is an element of | |
| \(\subseteq\) | $\quad:\quad$\subseteq
|
$\qquad$is a subset of | |
| \(\subsetneq\) | $\quad:\quad$\subsetneq
|
$\qquad$is a proper subset of | |
| \(\O\) | $\quad:\quad$\O
|
$\qquad$the empty set: $\set {}$ | |
| \(\powerset S\) | $\quad:\quad$\powerset S
|
$\qquad$the power set of the set $S$: $\powerset S = \set {T: T \subseteq S}$ | |
| \(p \land q\) | $\quad:\quad$p \land q
|
$\qquad$logical conjunction: $p$ and $q$ are both true | |
| \(p \lor q\) | $\quad:\quad$p \lor q
|
$\qquad$logical disjunction: either $p$ or $q$ is true (or both are) | |
| \(\forall\) | $\quad:\quad$\forall
|
$\qquad$the universal quantifier: for all | |
| \(\exists\) | $\quad:\quad$\exists
|
$\qquad$the existential quantifier: there exists | |
| \(S \setminus T\) | $\quad:\quad$S \setminus T
|
$\qquad$set difference: the elements of $S$ which are not in $T$ (when $S$ and $T$ are sets) | |
| \(S \symdif T\) | $\quad:\quad$S \symdif T
|
$\qquad$symmetric difference: the elements of $S$ and $T$ which are not in both (when $S$ and $T$ are sets) | |
| \(a \divides b\) | $\quad:\quad$a \divides b
|
$\qquad$$a$ is a divisor of $b$ (when $a$ and $b$ are integers) | |
| \(a \nmid b\) | $\quad:\quad$a \nmid b
|
$\qquad$$a$ is not a divisor of $b$ |
Some basic algebraic and arithmetic notation which may not be universal in schools:
| \(x !\) | $\quad:\quad$x !
|
$\qquad$$x$ factorial: $x \times \paren {x - 1} \times \paren {x - 2} \times \cdots \times 2 \times 1$ | |
| \(0 \cdotp \dot 3\) | $\quad:\quad$0 \cdotp \dot 3
|
$\qquad$"$0 \cdotp 3$ recurring", that is: $0 \cdotp 33333 \ldots$ | |
| \(0 \cdotp \dot 234 \dot 5\) | $\quad:\quad$0 \cdotp \dot 234 \dot 5
|
$\qquad$Similarly: that is: $0 \cdotp 234523452345 \ldots$ |
Some compound constructions:
- Let $\GF \in \set {\R, \C}$.
This means:
- Let $\GF$ be either the set of real numbers $\R$ or the set of complex numbers $\C$.