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  "body": "\n## Summary\n\nThe height of a [[partially ordered set|0QV2JS9RJ3]] is the largest number of elements of a [[chain|0S8FE7ZMFM]] in it.\nIt is the number of elements in the longest sequence of elements each strictly above the previous one.\nBy [[Mirsky's theorem|5VPXR3RDF1]], for a finite poset it is also the least number of antichains that cover the poset.\n\n## Explanations\n\n### L1 human\n\nDraw a poset with smaller elements lower down.\nThe height counts the elements on the tallest path that only goes upward.\nIn the divisors of $12$ ordered by divisibility, the path $1, 2, 4, 12$ has $4$ elements, and no chain is longer, so the height is $4$.\nAn antichain has height $1$.\n",
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