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  "body": "\n## Definition\n\nLet $A$ be a set.\nA preorder on $A$ is a [[binary relation|08EJC6Q25H]] $\\le$ on $A$ that is [[reflexive|0XEGNW851S]] and [[transitive|0CYRECG2YQ]]. For all $a, b, c \\in A$:\n\n1. $a \\le a$;\n2. $a \\le b$ and $b \\le c$ imply $a \\le c$.\n\n## Remarks\n\nDivisibility on $\\mathbb{Z}$ is a preorder. It is not antisymmetric, because $2 \\mid -2$ and $-2 \\mid 2$.\nAn antisymmetric preorder is a [[partial order|011C29Q1S1]].\nFor a preorder, $a \\le b$ and $b \\le a$ together define an [[equivalence relation|0SGTMBEWRF]]. The preorder gives a partial order on the [[quotient set|0ZVHXDSZC7]].\n\n## Explanations\n\n### L1 human\n\nCompare people by height with \"is at most as tall as\".\nThis is a preorder: two different people can have the same height.\n",
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