\begin{definition}[Definition:Limit of Real Function/Limit at Infinity/Negative/Decreasing Without Bound]
Let $f$ be a real function defined on an open interval $\openint \gets a$.
Suppose that:
:$\forall M \in \R_{<0}: \exists N \in \R_{<0}: x < N \implies \map f x < M$
for $M$ sufficiently large in magnitude.
Then we write:
:$\ds \lim_{x \mathop \to -\infty} \map f x = +\infty$
or
:$\map f x \to +\infty \ \text{as} \ x \to -\infty$
This is voiced:
:'''$\map f x$ decreases without bound as $x$ decreases without bound'''.
or:
:'''$\map f x$ tends to minus infinity as $x$ tends to minus infinity'''.
\end{definition}