> [!NOTE] Definition (Limits at infinity) > Let $f:\mathbb{R}\to \mathbb{R}$ be a [[Real Function|real function]]. We write $\lim_{ x \to \infty } f(x) = L$ iff for every $\varepsilon>0$ there exists $N> 0$ such that for all $x\in \mathbb{R},$ $x>N \implies |f(x)-L|<\varepsilon.$