551: Convex Subset of Real Vectors Space

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definition of convex subset of real vectors space

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Topics

About: vectors space

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Structured Description
• 2: Natural Language Description

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Starting Context

• The reader knows a definition of %field name% vectors space.

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Target Context

• The reader will have a definition of convex subset of real vectors space.

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Orientation

There is a list of definitions discussed so far in this site.

There is a list of propositions discussed so far in this site.

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Main Body

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1: Structured Description

Here is the rules of Structured Description.

Entities:
$V$: $\in \text{ the real vectors spaces }$
$\ast S$: $\subseteq V$
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Conditions:
$\mathrm{\forall }{p}_1,p_2\in S,\mathrm{\forall }t\in \mathbb{R}\text{ such that }0\le t\le 1(p_1+t(p_2-p_1)\in S)$.
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2: Natural Language Description

For any real vectors space, $V$, any subset, $S\subseteq V$, such that $\mathrm{\forall }{p}_1,p_2\in S,\mathrm{\forall }t\in \mathbb{R}\text{ such that }0\le t\le 1(p_1+t(p_2-p_1)\in S)$

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References

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