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  "body": "\n## Summary\n\nA partially ordered set satisfies the Jordan–Dedekind chain condition when, between any two comparable elements, all [[maximal chains|3AX549FFFM]] have the same finite length.\nIt is the property behind the Jordan–Hölder theorem, which says that composition series of a group have the same length.\nFor a finite poset with a least element, it is the same as being a [[graded poset|1C7TKGTB2F]].\n\n## Explanations\n\n### L1 human\n\nThink of climbing from one element to a higher one by steps that cannot be split further.\nThe condition says that every such climb takes the same number of steps, whatever route is chosen.\nIn the divisors of $12$, every climb from $1$ to $12$ by single prime factors takes $3$ steps, such as $1, 2, 4, 12$ or $1, 3, 6, 12$.\n",
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