Order Isomorphism is Equivalence Relation/Proof 2
Jump to navigation
Jump to search
Theorem
Order isomorphism between ordered sets is an equivalence relation.
So any given family of ordered sets can be partitioned into disjoint classes of isomorphic sets.
Proof
An ordered set is a relational structure where order isomorphism is a special case of relation isomorphism.
The result follows directly from Relation Isomorphism is Equivalence Relation.
$\blacksquare$