To prove that a given relation is a well ordering, we may show that it has the three properties of a partial order and the two additional properties that make it a well ordering. There are other ways to describe a well ordering.
(a) Prove that a partial order R on a set A is a well ordering if and only if every nonempty subset of A has a smallest element.
(b) Prove that a relation R on a set A is a well ordering if and only if every nonempty subset B of A contains a unique element that is R-related to every element of B.
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