Accumulation points at infinity

Remark — Accumulation points at infinity

We say that $+\infty$ is an accumulation point of $D$ if $D$ is unbounded above, that is, if for every $M>0$ there exists $x\in D$ with $x>M$. Similarly for $-\infty$ (unbounded below).

It is precisely this notion that gives meaning to limits of the form $\lim_{x\to+\infty}f(x)$: we can “let $x$ tend to infinity” only if the domain contains values of $x$ as large as we wish.

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Topics: Limits
Concepts: Infinity · Accumulation point