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  "body": "\n## Summary\n\nThe width of a [[partially ordered set|0QV2JS9RJ3]] is the largest size of an [[antichain|03HF498P1J]] in it.\nIt measures how many elements can be pairwise incomparable at the same time.\nBy [[Dilworth's theorem|GT224XDA4E]], for a finite poset it is also the least number of chains that cover the poset.\n\n## Explanations\n\n### L1 human\n\nDraw a poset with smaller elements lower down.\nThe width is the largest number of elements that sit side by side, with no two of them related.\nA chain has width $1$.\nIn the subsets of $\\set{1, 2, 3}$ ordered by inclusion, the three one-element subsets form an antichain, and no antichain is larger, so the width is $3$.\n",
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