\begin{definition}[Definition:Open Set/Real Analysis/Real Numbers]
Let $I \subseteq \R$ be a subset of the set of real numbers.
Then $I$ is '''open (in $\R$)''' {{iff}}:
: $\forall x_0 \in I: \exists \epsilon \in \R_{>0}: \openint {x_0 - \epsilon} {x_0 + \epsilon} \subseteq I$
where $\openint {x_0 - \epsilon} {x_0 + \epsilon}$ is an open interval.
Note that $\epsilon$ may depend on $x_0$.
\end{definition}