Definition:Limit of Real Function/Limit at Infinity/Negative/Increasing Without Bound

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Definition

Let $f$ be a real function defined on an open interval $\openint \gets a$.

Suppose that:

$\forall M \in \R_{>0}: \exists N \in \R_{<0}: \forall x < N : \map f x > M$

for $M$ sufficiently large.

Then we write:

$\ds \lim_{x \mathop \to -\infty} \map f x = +\infty$

or

$\map f x \to +\infty$ as $x \to -\infty$

This is voiced:

$\map f x$ increases without bound as $x$ decreases without bound.

or:

$\map f x$ tends to (plus) infinity as $x$ tends to minus infinity.


Also see


Sources