The ascending chain condition on P is equivalent to the maximum condition: every nonempty subset of P has a maximal element. Similarly, the descending chain condition is equivalent to the minimum condition: every nonempty subset of P has a minimal element.
Every finite poset satisfies both ACC and DCC.
A totally ordered set that satisfies the descending chain condition is called a well-ordered set
See also Noetherian and Artinian.
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