definition of convex subset of real vectors space
Topics
About: vectors space
The table of contents of this article
- Starting Context
- Target Context
- Orientation
- Main Body
- 1: Structured Description
- 2: Natural Language Description
Starting Context
- The reader knows a definition of %field name% vectors space.
Target Context
- The reader will have a definition of convex subset of real vectors space.
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.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\( V\): \(\in \text{ the real vectors spaces }\)
\(*S\): \(\subseteq V\)
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Conditions:
\(\forall p_1, p_2 \in S, \forall t \in \mathbb{R} \text{ such that } 0 \le t \le 1 (p_1 + t (p_2 - p_1) \in S)\).
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2: Natural Language Description
For any real vectors space, \(V\), any subset, \(S \subseteq V\), such that \(\forall p_1, p_2 \in S, \forall t \in \mathbb{R} \text{ such that } 0 \le t \le 1 (p_1 + t (p_2 - p_1) \in S)\)
