Definition:Continuous Real Function/Left-Continuous

Definition
Let $S \subseteq \R$ be an open subset of the real numbers $\R$.

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

Let $x_0 \in S$.

Then $f$ is said to be left-continuous at $x_0$ or continuous from the left at $x_0$ iff:


 * $\displaystyle \lim_{x \to x_0^-} f \left({x}\right) = f \left({x_0}\right)$

where $\displaystyle \lim_{x \to x_0^-}$ is a limit from the left.

Furthermore, $f$ is said to be left-continuous iff:


 * $\forall x_0 \in S$, $f$ is left-continuous at $x_0$

Also see

 * Right-Continuous
 * Continuous Real Function