Hasse diagram of either can be converted to a Hasse diagram of the other by simply relabeling the vertices.

Definition

Formally, given two posets and , an order isomorphism from to is a bijective function from to with the property that, for every and in , if and only if . That is, it is a bijective order-embedding.

It is also possible to define an order isomorphism to be a surjective

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