Limit

Relevant Classe: Math 297

Summary

Suppose $(V,⟨,{⟩}_V)$ and $(W,⟨,{⟩}_W)$ are finite dimensional inner product spaces. Suppose $A\subseteq V$, $\vec{v}$ is a limit point of $A$, $\vec{w}\in W$, and $f:A\to W$ is a function. We say ${\lim }_{\vec{x}\to \vec{v}}f(\vec{x})=\vec{w}$ provided that for all $\epsilon >0$ there is a $\delta >0$ such that $\text{whenever }\vec{x}\in A\text{ and }0<\Vert \vec{x}-\vec{v}{\Vert }_V<\delta ,\text{ it follows that }\Vert f(\overrightarrow{(}x)-\vec{w})\Vert <\epsilon$