Function Limit

Last updated Nov 1, 2022

Let $(M,d_{1})$ and $(N, d_{2})$ be two Metric Spaces. Let $f: M \to N$ be a Function. Suppose there exists $y \in N$ s.t. $\forall \epsilon > 0$ $\exists \delta >0$ s.t. $\forall u \in B_{\delta}(x) \setminus {x}$ $$d_{2}(f(u), f(y)) < \epsilon$$ Then we call $y$ the Function Limit of $f$ at $x$.

• Real Numbers