Order Isomorphism is Equivalence Relation/Proof 2

From ProofWiki
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.

$\blacksquare$