$ \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\abs}[2][]{\left\lvert#2\right\rvert_{\text{#1}}} \newcommand{\ket}[1]{\left\lvert#1 \right.\rangle} \newcommand{\bra}[1]{\langle\left. #1\right\rvert} \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\dd}{\text{d}} \newcommand{\dv}[2]{\frac{\dd #1}{\dd #2}} \newcommand{\pdv}[2]{\frac{\partial}{\partial #1}} $
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Sequential Converges

Let $A\subseteq\mathbb{R}^n$ and $f:A\to\mathbb{R}^m$ for any point $\vec{a}\in A$, the following are equivalent:
  1. $f$ is continuous at $\vec{a}$
  2. $\lim_{k\to\infty}f(\vec{x}_k)=f(\vec{a})$ for every seqyence in $A$ such that $\lim_{k\to\infty}\vec{x}_k=\vec{a}$.

Concepts

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Hypothesis

Coming soon

Results

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Proof

Coming soon

Sequential Converges

Let $A\subseteq\mathbb{R}^n$ and $f:A\to\mathbb{R}^m$ for any point $\vec{a}\in A$, the following are equivalent:
  1. $f$ is continuous at $\vec{a}$
  2. $\lim_{k\to\infty}f(\vec{x}_k)=f(\vec{a})$ for every seqyence in $A$ such that $\lim_{k\to\infty}\vec{x}_k=\vec{a}$.

Concepts

Coming soon

Hypothesis

Coming soon

Results

Coming soon

Proof

Coming soon
FullPage
result
concepts
hypothesis
implications
proof
FullPage
result
concepts
hypothesis
implications
proof

Sequential Converges

Let $A\subseteq\mathbb{R}^n$ and $f:A\to\mathbb{R}^m$ for any point $\vec{a}\in A$, the following are equivalent:
  1. $f$ is continuous at $\vec{a}$
  2. $\lim_{k\to\infty}f(\vec{x}_k)=f(\vec{a})$ for every seqyence in $A$ such that $\lim_{k\to\infty}\vec{x}_k=\vec{a}$.

Concepts

Coming soon

Hypothesis

Coming soon

Results

Coming soon

Proof

Coming soon

Sequential Converges

Let $A\subseteq\mathbb{R}^n$ and $f:A\to\mathbb{R}^m$ for any point $\vec{a}\in A$, the following are equivalent:
  1. $f$ is continuous at $\vec{a}$
  2. $\lim_{k\to\infty}f(\vec{x}_k)=f(\vec{a})$ for every seqyence in $A$ such that $\lim_{k\to\infty}\vec{x}_k=\vec{a}$.

Concepts

Coming soon

Hypothesis

Coming soon

Results

Coming soon

Proof

Coming soon
FullPage
result
concepts
hypothesis
implications
proof