die gemeinsame Punktmenge zweier (analog mehrerer) Intervalle, falls diese „überlappen“, ansonsten die leere Menge.

Formal definiert bedeutet dies: Der Durchschnitt zweier reeller Intervalle \({\bf{\text{a}}}\,=\,[\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{a},\bar{a}]\) und \({\bf{\text{b}}}\,=\,[\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{b},\bar{b}]\) ist

\begin{eqnarray}{\bf{a}}\cap {\bf{b}}=\left\{\begin{array}{c}[\rm{max}\{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{a},\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{b}\},\rm{min}\{\bar{a},\bar{b}\}]\\ \varnothing, \end{array}\right.\\ \rm{falls}\quad\left\{\begin{array}\rm{max}\{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{a},\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{b}\}\le \rm{min}\{\bar{a},\bar{b}\}\\ \rm{max}\{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{a},\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{b}\}\gt \rm{min}\{\bar{a},\bar{b}\}\end{array}\right.\end{eqnarray}