# Symbols: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$$a is a divisor of b (when a and b are integers) $a \nmid b$ \quad:\quada \nmid b \qquad$$a$ is not a divisor of $b$
 $x !$ $\quad:\quad$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: $0 \cdotp 234523452345 \ldots$