# Definition:Neighborhood of Infinity (Real Analysis)

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## Contents

## Definition

### Neighborhood of Positive Infinity

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

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