# Definition:Neighborhood of Infinity (Real Analysis)

## 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.