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:


 * $$N_\epsilon \left({\alpha}\right) \ \stackrel {\mathbf {def}} {=\!=} \ \left({\alpha - \epsilon \, . \, . \, \alpha + \epsilon}\right)$$

Linguistic Note
The UK English spelling of this is neighbourhood.