Real numbers/Intervals/Definition

For real numbers ${\displaystyle {}a,b}$, ${\displaystyle {}a\leq b}$, we call

1. ${\displaystyle {}[a,b]={\left\{x\in \mathbb {R} \mid x\geq a{\text{ and }}x\leq b\right\}}}$ the closed interval.
2. ${\displaystyle {}]a,b[={\left\{x\in \mathbb {R} \mid x>a{\text{ and }}x<b\right\}}}$ the open interval.
3. ${\displaystyle {}]a,b]={\left\{x\in \mathbb {R} \mid x>a{\text{ and }}x\leq b\right\}}}$ the half-open interval (closed on the right).
4. ${\displaystyle {}[a,b[={\left\{x\in \mathbb {R} \mid x\geq a{\text{ and }}x<b\right\}}}$ the half-open interval (closed on the left).