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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 $m \\in S$ is a minimal element of $S$ when no $s \\in S$ satisfies $s \u003c m$.\nEquivalently, for each $s \\in S$, $s \\le m$ implies $s = m$.\n\n## Remarks\n\nIt is the [[maximal element|0TZEEFTNCC]] for the reversed order $\\ge$.\nIn $\\{2, 3, 4, 6, 9\\}$ under divisibility, the minimal elements are $2$ and $3$.\nA [[well-founded relation|0230ECX1Q5]] is one in which each nonempty subset has a minimal element.\n\n## Explanations\n\n### L1 human\n\nA minimal element has nothing below it.\nAmong the integers greater than $1$ under divisibility, the minimal elements are the primes.\n",
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