# Definition:Neighborhood of Infinity (Real Analysis)

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## Definition

### Neighborhood of Positive Infinity

A **neighborhood of $+\infty$** is a subset of the set of real numbers $\R$ which contains an interval $\openint a \to$ for some $a \in \R$.

That is, a subset which contains all sufficiently large real numbers.

### Neighborhood of Negative Infinity

A **neighborhood of $-\infty$** is a subset of the set of real numbers $\R$ wich contains an interval $\openint \gets a$ for some $a \in \R$.

That is, a subset which contains all sufficiently large negative real numbers.