definition of chain of partially-ordered set
Topics
About: set
The table of contents of this article
Starting Context
- The reader knows a definition of partially-ordered set.
Target Context
- The reader will have a definition of chain of partially-ordered 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:
\( S\): \(\in \{\text{ the partially-ordered sets }\}\)
\(*C\): \(\subseteq S\)
//
Conditions:
\(\forall c_1, c_2 \in C (c_1 \le c_2 \lor c_2 \lt c_1)\)
//
2: Note
For any set, the ordering as containment is a partial ordering, by the proposition that any set with the ordering as containment is a partially-ordered set, and "chain" of the set without ordering specified is a chain with respect to the containment ordering.
