Definition:Continuous Real Function/Right-Continuous/Point

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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 right-continuous at $x_0$ if and only if the limit from the right of $f \left({x}\right)$ as $x \to x_0$ exists and:

$\displaystyle \lim_{\substack{x \mathop \to x_0^+ \\ x_0 \mathop \in A}} f \left({x}\right) = f \left({x_0}\right)$

where $\displaystyle \lim_{x \mathop \to x_0^+}$ is a limit from the right.


Furthermore, $f$ is said to be right-continuous if and only if:

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


Also known as

A function which is right-continuous (either at a point or generally) is also seen referred to as continuous from the right.


Also see


Sources