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 $b$ 