Definition:Real Interval/Notation/Conventional

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Definition

These are the notations usually seen for real intervals:

\(\displaystyle \left ({a, b}\right)\) \(:=\) \(\displaystyle \set {x \in \R: a < x < b}\) Open real interval
\(\displaystyle \left [{a, b}\right)\) \(:=\) \(\displaystyle \set {x \in \R: a \le x < b}\) Half-open real interval
\(\displaystyle \left ({a, b}\right]\) \(:=\) \(\displaystyle \set {x \in \R: a < x \le b}\) Half-open real interval
\(\displaystyle \left [{a, b}\right]\) \(:=\) \(\displaystyle \set {x \in \R: a \le x \le b}\) Closed real interval

but they can be confused with other usages for this notation.

In particular, there exists the danger of taking $\paren {a, b}$ to mean an ordered pair.