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 $\R$ 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.


Also see