\begin{definition}[Definition:Continuous Real Function/Right-Continuous]
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 '''right-continuous at $x_0$''' {{iff}} the limit from the right of $\map f x$ as $x \to x_0$ exists and:
:$\ds \lim_{\substack {x \mathop \to x_0^+ \\ x_0 \mathop \in A}} \map f x = \map f {x_0}$
where $\ds \lim_{x \mathop \to x_0^+}$ is a limit from the right.
Furthermore, $f$ is said to be '''right-continuous''' {{iff}}:
:$\forall x_0 \in S$, $f$ is '''right-continuous at $x_0$'''
\end{definition}