definition of \(d\)-system on set
Topics
About: set
The table of contents of this article
Starting Context
- The reader knows a definition of power set of set.
Target Context
- The reader will have a definition of \(d\)-system on 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:
\( S\): \(\in \{\text{ the sets }\}\)
\(*D\): \(\subseteq Pow (S)\)
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Conditions:
\(S \in D\)
\(\land\)
\(\forall d_1, d_2 \in D \text{ such that } d_1 \subseteq d_2 (d_2 \setminus d_1 \in D)\)
\(\land\)
\(\forall s: \mathbb{N} \to D \text{ such that } \forall n \in \mathbb{N} (s (n) \subseteq s (n + 1)) (\cup_{n \in \mathbb{N}} s (n) \in D)\)
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