# Definition:Real Interval/Notation/Unbounded Intervals

Some authors (sensibly, perhaps) prefer not to use the $\infty$ symbol and instead use $\to$ and $\gets$ for $+\infty$ and $-\infty$ repectively.
 $\displaystyle \hointr a \to$ $:=$ $\displaystyle \set {x \in \R: a \le x}$ $\displaystyle \hointl \gets a$ $:=$ $\displaystyle \set {x \in \R: x \le a}$ $\displaystyle \openint a \to$ $:=$ $\displaystyle \set {x \in \R: a < x}$ $\displaystyle \openint \gets a$ $:=$ $\displaystyle \set {x \in \R: x < a}$ $\displaystyle \openint \gets \to$ $:=$ $\displaystyle \set {x \in \R} = \R$
 $\displaystyle \left [{a, \to} \right]$ $=$ $\displaystyle \set {x \in \R: a \le x}$ $\displaystyle \left [{\gets, a} \right]$ $=$ $\displaystyle \set {x \in \R: x \le a}$ $\displaystyle \left ]{\, a, \to} \right]$ $=$ $\displaystyle \set {x \in \R: a < x}$ $\displaystyle \left [{\gets, a \,} \right[$ $=$ $\displaystyle \set {x \in \R: x < a}$