Order Isomorphism is Equivalence Relation/Proof 1

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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


Follows directly from Identity Mapping is Order Isomorphism.


Follows directly from Inverse of Order Isomorphism is Order Isomorphism.


Follows directly from Composite of Order Isomorphisms is Order Isomorphism.

$\blacksquare$


Sources