Definition:Neighborhood (Real Analysis)/Epsilon

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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:

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

where $\epsilon \in \R_{>0}$ is a (strictly) positive real number.

Also see

Linguistic Note

The UK English spelling of neighborhood is neighbourhood.