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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: $0 \cdotp 234523452345 \ldots$