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  "body": "\n## Definition\n\nLet $(P, \\le)$ be a [[partially ordered set|011C29Q1S1]].\nA subset $A$ of $P$ is an antichain when, for all $a, b \\in A$ with $a \\neq b$, neither $a \\le b$ nor $b \\le a$.\n\n## Remarks\n\nIn the power set of $\\{1, 2, 3\\}$, the set $\\{\\{1\\}, \\{2\\}, \\{3\\}\\}$ is an antichain.\nA chain and an antichain have at most one common element.\nThe largest size of an antichain is the width of the poset.\n\n## Explanations\n\n### L1 human\n\nAn antichain is the opposite of a [[chain|0GP9ASVQ1X]]: its elements are side by side.\nUnder divisibility, the primes form an antichain, because no prime divides another prime.\n",
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