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  "body": "\n## Summary\n\nIn a [[partially ordered set|011C29Q1S1]], an element $y$ covers an element $x$ when $x \u003c y$ and nothing lies strictly between them.\nThe covering relation records the immediate steps of the order.\nFor a finite poset it determines the whole order, and it is exactly what a [[Hasse diagram|00EYM7MDKS]] draws.\n\n## Explanations\n\n### L1 human\n\nThe element $y$ covers $x$ when $y$ is the next step up from $x$, with no element in between.\nIn the integers, $n + 1$ covers $n$.\nIn the rational numbers nothing covers anything, because between two rationals there is always a third.\nFor the subsets of $\\set{1, 2, 3}$ ordered by inclusion, $\\set{1, 2}$ covers $\\set{1}$, but $\\set{1, 2, 3}$ does not cover $\\set{1}$.\n",
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