Definition:Real Interval/Notation/Reverse-Bracket

Definition

In order to avoid the ambiguity problem arising from the conventional notation for intervals where an open real interval can be confused with an ordered pair, some authors use the reverse-bracket notation for open and half-open intervals:

\(\ds \left ] {\, a, b} \right [\)

\(:=\)

\(\ds \set {x \in \R: a < x < b}\)

Open real interval

\(\ds \left [ {a, b} \right [\)

\(:=\)

\(\ds \set {x \in \R: a \le x < b}\)

Half-open on the right

\(\ds \left ] {\, a, b} \right ]\)

\(:=\)

\(\ds \set {x \in \R: a < x \le b}\)

Half-open on the left

These are often considered to be both ugly and confusing, and hence are limited in popularity.