# Definition:Real Interval/Notation/Conventional

 $\displaystyle \left ({a, b}\right)$ $:=$ $\displaystyle \set {x \in \R: a < x < b}$ 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
In particular, there exists the danger of taking $\paren {a, b}$ to mean an ordered pair.