Interval notation. Let $a, b$ be real numbers.

A set $I$ of real numbers is an interval iff for all $x,y\in I$ all real numbers between $x$ and $y$ are also in $I$.

The open interval $(a,b)=$ $\{x\in\m R\ |\ a< x< b\}$

The closed interval $[a,b]=$ $\{x\in\m R\ |\ a\le x\le b\}$

The half-open interval $(a,b]=$ $\{x\in\m R\ |\ a< x\le b\}$

The half-open interval $[a,b)=$ $\{x\in\m R\ |\ a\le x< b\}$

$(a,\infty)=$ $\{x\in\m R\ |\ a< x\}$

$(-\infty,b]=$ $\{x\in\m R\ |\ x\le b\}$

$(-\infty,\infty)=$ $\m R$ (the real line)