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  "body": "\n## Summary\n\nA partially ordered set satisfies the descending chain condition when every decreasing sequence of its elements is eventually constant.\nIt is the dual of the [[ascending chain condition|0GZ6Y1H4RN]].\nApplied to the ideals of a ring, it defines [[Artinian rings|20QEAM8AX2]]; applied to submodules, it defines [[Artinian modules|YQNZTQGP1X]].\nFor posets it is equivalent, under the axiom of dependent choice, to being a [[well-founded order|55WD0H03CZ]].\n\n## Explanations\n\n### L1 human\n\nPicture going down a staircase in a poset, one step at a time, never going back up.\nThe descending chain condition says that you must stop moving after finitely many real steps.\nThe natural numbers satisfy it, since you cannot go down from $10$ more than ten times.\nThe integers do not: $0 \u003e -1 \u003e -2 \u003e \\cdots$ goes down forever.\n",
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