Alternate Characterization of Continuity

Let $A\subseteq\mathbb{R}^n$ and let $f:A\to\mathbb{R}^m$. For any point $\vec{a}\in A\cap A^a$, the function $f$ is continuous at $\vec{a}$ if and only if $\lim_{\vec{x}\to\vec{a}}f(\vec{x})=f(\vec{a})$.

Concepts

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If

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Only If

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Proof

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Related

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Alternate Characterization of Continuity

Let $A\subseteq\mathbb{R}^n$ and let $f:A\to\mathbb{R}^m$. For any point $\vec{a}\in A\cap A^a$, the function $f$ is continuous at $\vec{a}$ if and only if $\lim_{\vec{x}\to\vec{a}}f(\vec{x})=f(\vec{a})$.

Concepts

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If

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Only If

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Proof

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Related

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