\begin{definition}[Definition:Limit of Real Function/Limit at Infinity/Positive]
Let $f$ be a real function defined on an open interval $\openint a \to$.
Let $L \in \R$.
$L$ is the '''limit of $f$ at infinity''' {{iff}}:
:$\forall \epsilon \in \R_{>0}: \exists c \in \R: \forall x > c : \size {\map f x - L} < \epsilon$
This is denoted as:
:$\ds \lim_{x \mathop \to \infty} \map f x = L$
\end{definition}