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.