limit point

[Math] Limit of a multi-variate function and Limit Point

Definition of Limit [= ($\epsilon$-$\delta$) definition] Assume that $S\subseteq \mathbb{R}^n$, and that $f:S\to \mathbb{R}$ is a mutivariate function. The statement $$ \underset{\textbf{x} \to \textbf{a}}{\lim} f (\textbf{x})= L$$ is defined to mean that $$\begin{equation}\label{lim.def} \forall \varepsilon >0, \ \ \exists \delta>0 \quad\mbox{ such that if } \mathbf x \in S \mbox{ and } 0 < || ..