Definition:Limit of Real Function/Limit at Infinity/Positive

Definition
Let $f: \R \to \R$ be a real function.

Let $L \in \R$.

$L$ is the limit of $f$ at infinity :
 * $\forall \epsilon \in \R_{>0}: \exists c \in \R: \forall x > c : \size {\map f x - L} < \epsilon$

This is denoted as:
 * $\displaystyle \lim_{x \mathop \to \infty} \map f x = L$