> [!NOTE] Definition (Left limits) > Let $I$ be an [[Open Real Interval|open interval]]. Let $c\in I.$ Let $f$ be a [[Real Function|real function]] defined on $I,$ except possibly at $c.$ Then $L$ is the limit of $f(x)$ as $x$ approaches $c$ from the left, denoted $\lim_{ x \to c^{-} } f(x) = L,$ iff for every $\varepsilon>0$, there exists $\delta>0$ such that $x\in(c-\delta,c) \implies |f(x)-L|<\varepsilon.$ >