Symbols:Glossary

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 $b$