Equivalent definition for an open interval around a point in $\mathbb{R}$
If $\ I\subset\mathbb{R}\ $ is an interval, then $\ I = (\inf (I), \sup (I))\ = (a-\delta, a+\delta),\ $ where
$a=\frac{\inf (I) + \sup (I)}{2}\ $ and $\ \delta = \ \frac{\sup (I) - \inf (I)}{2}.$
You can confirm via calculation that $\ a-\delta = \inf(I)\ $ and that $\ a+\delta = \sup(I).$