# Definition:Neighborhood (Real Analysis)/Open Subset

< Definition:Neighborhood (Real Analysis)(Redirected from Definition:Neighborhood of Real Number)

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## Definition

Let $\alpha \in \R$ be a real number.

Let $N_\alpha$ be a subset of $\R$ which contains (as a subset) an open real set which itself contains (as an element) $\alpha$.

Then $N_\alpha$ is a **neighborhood** of $\alpha$.

## Linguistic Note

The UK English spelling of **neighborhood** is **neighbourhood**.