Infinite limit

Definition

Let $D \subseteq \mathbb{R}$ , let $f \colon D \to \mathbb{R}$ , and let $a$ be a limit point of $D$ . The notation $f(x) \to +\infty$ as $x \to a$ means that for each real $M$ there is $\delta > 0$ with $f(x) > M$ for all $x \in D$ with $0 < |x - a| < \delta$ . The definition of $f(x) \to -\infty$ is the same, with $f(x) < M$ .

Remarks

An infinite limit is not a limit in the sense of limit of a function, which requires a real value $L$ . For example, $1/x^2 \to +\infty$ as $x \to 0$ . The same idea gives $f(x) \to +\infty$ as $x \to +\infty$ . An example is $f(x) = x^2$ .

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Limit point of a set definition
Limit of a function definition
Infinite limit definition

Tag	`08NM8KQPDQ`
URI	`m2://08NM8KQPDQ`
Kind	definition
Writing	W0 stub
MSC	26A03
Defines	Infinite limit
Uses	Limit of a function

Infinite limit

Definition

Remarks

Reading path

Further reading

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