# Definition:Open Neighborhood/Real Analysis

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## Definition

### Real Numbers

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

Let $I \subseteq \R$ be a subset.

Then $I$ is an **open neighborhood of $x$** if and only if $I$ is open and $I$ is a neighborhood of $x$.

### Real Euclidean Space

Let $n\geq1$ be a natural number.

Let $x\in\R^n$.

Let $I \subseteq \R$ be a subset.

Then $I$ is an **open neighborhood of $x$** if and only if $I$ is open and $I$ is a neighborhood of $x$.