6.8 Partial orders (optional)
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Introduction and example
A partial order is a relation between elements of a set. You already know an instance of a partial order, namely ≤ on numbers. For example:
The three axioms defining partial orders
In the following, think of a, b, and c as natural numbers. Then think of the following three axioms in terms of natural numbers:
Application to subtype relation
All of these axioms are satisfied by every partial order. Since the subtype relation on a type hierarchy is a partial order, these axioms are also satisfied by the subtype relation.
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