$ \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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Let $X$ be a nonempty subset of $\mathbb{R}^n$. Then $X$ is convex if for any $\vec{x}, \vec{y}\in X$, and any $t\in[0, 1]$, the point $\vec{x}+t(\vec{y}-\vec{x})$ is in $X$.

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Let $X$ be a nonempty subset of $\mathbb{R}^n$. Then $X$ is convex if for any $\vec{x}, \vec{y}\in X$, and any $t\in[0, 1]$, the point $\vec{x}+t(\vec{y}-\vec{x})$ is in $X$.

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FullPage
definition
concepts
used in
hypothesis
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FullPage
definition
concepts
used in
hypothesis
results
Let $X$ be a nonempty subset of $\mathbb{R}^n$. Then $X$ is convex if for any $\vec{x}, \vec{y}\in X$, and any $t\in[0, 1]$, the point $\vec{x}+t(\vec{y}-\vec{x})$ is in $X$.

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Let $X$ be a nonempty subset of $\mathbb{R}^n$. Then $X$ is convex if for any $\vec{x}, \vec{y}\in X$, and any $t\in[0, 1]$, the point $\vec{x}+t(\vec{y}-\vec{x})$ is in $X$.

Concepts

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Used In

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Hypothesis

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FullPage
definition
concepts
used in
hypothesis
results