definition of saturation of subset of set with equivalence relation
Topics
About: set
The table of contents of this article
Starting Context
- The reader knows a definition of equivalence relation on set.
Target Context
- The reader will have a definition of saturation of subset of set with equivalence relation.
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:
\( S'\): \(\in \{\text{ the sets }\}\), with any equivalence relation, \(\sim'\)
\( S\): \(\subseteq S'\)
\(*Sat (S, \sim')\): \(= \{s' \in S' \vert \exists s \in S (s \sim' s')\}\)
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Conditions:
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2: Note
\(S \subseteq Sat (S, \sim')\), because for each \(s \in S\), there is \(s \in S\) such that \(s \sim' s\), so, \(s \in Sat (S, \sim')\).
