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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 $l \\in S$ is the least element of $S$ when $l \\le s$ for each $s \\in S$.\n\n## Remarks\n\nAnother name is minimum. By antisymmetry, a set has at most one least element.\nEach nonempty subset of $\\mathbb{N}$ has a least element. This is the well-ordering principle of $\\mathbb{N}$. See [[well-order|0F1D6PK9RZ]].\nThe interval $(0, 1]$ in $\\mathbb{R}$ has no least element.\n\n## Explanations\n\n### L1 human\n\nThe least element is below all others.\nIn the power set of a set under $\\subseteq$, the least element is the empty set.\n",
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