$$ B^n(\vec{a},r) = \Big\lbrace \vec{x}\ |\ \vec{x} \in \mathbb{R}^n, ||\vec{x} - \vec{a}|| < r\Big\rbrace $$ then: $$ \lim_{x \to a}f(x)=A\ \ \ \stackrel{\mathrm{def}}{=}\ \ \ \forall\epsilon>0,\ \exist \delta > 0,\ s.t.\ \ B^n(\vec{a},\delta) \backslash \big\lbrace \vec{a} \big\rbrace \subset f^{-1}(B^n(A,\epsilon)) $$