definition of Euclidean set
Topics
About: set
The table of contents of this article
Starting Context
- The reader knows a definition of set.
Target Context
- The reader will have a definition of Euclidean set.
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:
\( d\): \(\in \mathbb{N} \setminus \{0\}\)
\(*\mathbb{R}^d\):
//
Conditions:
//
2: Note
The point is that \(\mathbb{R}^d\) is a pure set without any vectors space structure, any metric, any topology, or anything assumed.
Sometimes, it is important to be free from some additional structures usually presupposed onto \(\mathbb{R}^d\).
