\begin{definition}[Definition:Limit of Real Function/Limit at Infinity/Negative/Increasing Without Bound]
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'''.
\end{definition}