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.