\( \newcommand{\cat}[1] {\mathrm{#1}} \newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})} \newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}} \newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}} \newcommand{\betaReduction}[0] {\rightarrow_{\beta}} \newcommand{\betaEq}[0] {=_{\beta}} \newcommand{\string}[1] {\texttt{"}\mathtt{#1}\texttt{"}} \newcommand{\symbolq}[1] {\texttt{`}\mathtt{#1}\texttt{'}} \)

Intervals (of the reals), definition

Let \( a, b \in \mathbb{R}^* \) be extended real numbers.

We define the closed interval \( [a, b] \) by

We define the half-open intervals \( [a, b) \) and \( (a, b] \) by

And we define the open interval \( (a, b) \) by

We call \( a \) the [...] and \( b \) the [...].