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  "body": "\n## Definition\n\nLet $(P, \\le)$ be a [[partially ordered set|011C29Q1S1]].\nA subset $C$ of $P$ is a chain when, for all $a, b \\in C$, $a \\le b$ or $b \\le a$.\n\n## Remarks\n\nSo a chain is a subset on which $\\le$ is a [[total order|0316AYH1SC]].\nIn the power set of $\\mathbb{N}$, the sets $\\{0\\} \\subseteq \\{0, 1\\} \\subseteq \\{0, 1, 2\\} \\subseteq \\dots$ form a chain.\nChains are the key notion in [[Zorn's lemma|04RXTQA5ZA]] and in the [[Hausdorff maximal principle|0KM4KVR9MV]].\n\n## Explanations\n\n### L1 human\n\nA chain is a part of the order that lies on one line.\nIn the divisors of $12$, the set $\\{1, 2, 4, 12\\}$ is a chain, but $\\{2, 3\\}$ is not.\n",
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