Right Function Limit

Last updated Nov 1, 2022

Let $f: \mathbb{R} \to M$ be a Function where $(M, d)$ is a Metric Space and let $x \in \mathbb{R}$. Suppose there exists $y \in M$ s.t. $$\lim\limits_{u \to x} f{\big|}{[x, \infty)}(u) = y$$ where $f {\big|}{[x, \infty)}$ is the Function Restriction of $f$ to $[x, \infty)$. Then we call $y$ the Right Function Limit of $f$ at $x$. We denote it $$\lim_{u \downarrow x} f(u)$$

1. Applying the Heine Criterion to $[x, \infty)$ gives us the connection between Sequences in $[x, \infty)$ converging to $x$ and the Right Function Limit at $x$.

• Real Numbers
• Function Limit