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  "body": "\n## Definition\n\nLet $(P, \\le)$ be a partially ordered set and let $S$ be a subset of $P$.\nAn element $a$ of $P$ is an infimum, or greatest lower bound, of $S$ when these two conditions hold:\n\n1. $a$ is a [[lower bound|0B5H2V4JW8]] of $S$;\n2. if $m$ is a lower bound of $S$, then $m \\le a$.\n\nThe notation is $a = \\inf S$.\n\n## Remarks\n\nA set has at most one infimum.\nIn $\\mathbb{R}$, $\\inf \\{1/n : n \\ge 1\\} = 0$, and $0$ is not an element of this set.\nFor a subset $S$ of $\\mathbb{R}$, $\\inf S = -\\sup(-S)$ when one side exists, where $-S = \\{-s : s \\in S\\}$.\n\n## Explanations\n\n### L1 human\n\nThe infimum is the highest possible floor for a set.\nFor the set $\\{1, 1/2, 1/3, \\dots\\}$, every number at most $0$ is a floor, and $0$ is the highest of these, so the infimum is $0$.\n",
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