2024-04-21

550: Affine Subset of Real Vectors Space

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definition of affine subset of real vectors space

Topics


About: vectors space

The table of contents of this article


Starting Context



Target Context


  • The reader will have a definition of affine 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:
\( V\): \(\in \text{ the real vectors spaces }\)
\(*S\): \(\subseteq V\)
//

Conditions:
\(\forall p_1, p_2 \in S, \forall t \in \mathbb{R} (p_1 + t (p_2 - p_1) \in S)\).
//


2: Natural Language Description


For any real vectors space, \(V\), any subset, \(S \subseteq V\), such that \(\forall p_1, p_2 \in S, \forall t \in \mathbb{R} (p_1 + t (p_2 - p_1) \in S)\)


References


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