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  "body": "\n## Definition\n\nLet $(P, \\le)$ be a [[partially ordered set|011C29Q1S1]] and let $S$ be a [[subset|0FE8Q5S42Y]] of $P$.\nAn element $g \\in S$ is the greatest element of $S$ when $s \\le g$ for each $s \\in S$.\n\n## Remarks\n\nAnother name is maximum. By antisymmetry, a set has at most one greatest element.\nA greatest element is a [[maximal element|0TZEEFTNCC]] and an [[upper bound|0H5J02P8S9]] of $S$ that lies in $S$.\nThe interval $[0, 1)$ in $\\mathbb{R}$ has no greatest element.\n\n## Explanations\n\n### L1 human\n\nThe greatest element beats every other element of the set.\nIn $\\{1, 2, 3, 6\\}$ under divisibility, $6$ is the greatest element, because each element divides $6$.\n",
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