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  "body": "\n## Summary\n\nA strict partial order is a binary relation $\u003c$ that is irreflexive and transitive.\nIt is the \"strictly less than\" version of a [[partial order|011C29Q1S1]].\nStrict partial orders on a set correspond one to one with partial orders on the same set.\nSo either one can serve as the basic notion.\n\n## Explanations\n\n### L1 human\n\nA strict partial order says when one element is strictly below another.\nNo element is strictly below itself, and if $a$ is below $b$ and $b$ is below $c$, then $a$ is below $c$.\nSome pairs may be incomparable.\nFor example, \"is a proper subset of\" on the subsets of $\\set{1, 2}$ puts $\\emptyset$ below $\\set{1}$, but $\\set{1}$ and $\\set{2}$ are incomparable.\n",
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