Definition:Neighborhood (Real Analysis)/Epsilon

Definition
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:


 * $N_\epsilon \left({\alpha}\right) := \left({\alpha - \epsilon \, . \, . \, \alpha + \epsilon}\right)$

Linguistic Note
The UK English spelling of this is neighbourhood.