\begin{definition}[Definition:Neighborhood (Real Analysis)/Epsilon]
Let $\alpha \in \R$ be a real number.
On the real number line with the usual metric, the '''$\epsilon$-neighborhood''' of $\alpha$ is defined as the open interval:
:$\map {N_\epsilon} \alpha := \openint {\alpha - \epsilon} {\alpha + \epsilon}$
where $\epsilon \in \R_{>0}$ is a (strictly) positive real number.
\end{definition}