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  "body": "\n## Statement\n\nLet $S$ be a nonempty subset of the [[real numbers|08J2M1JYAG]] that is [[bounded above|0B5H2V4JW8]].\nThen $S$ has a [[supremum|0BTMQ04556]] in $\\mathbb{R}$.\n\n## Remarks\n\nIn the axiomatic approach, this is the axiom that distinguishes $\\mathbb{R}$ from the other ordered fields. In a construction of $\\mathbb{R}$, it is a theorem.\nThe ordered field $\\mathbb{Q}$ does not have this property: $\\{q \\in \\mathbb{Q} : q^2 \u003c 2\\}$ has no supremum in $\\mathbb{Q}$.\nThe axiom gives the [[existence of the infimum|0EDH403M21]] and the [[Archimedean property of the reals|0A3GWZ86AY]].\n\n## Explanations\n\n### L1 human\n\nThe real line has no holes.\nIf a set of real numbers has a ceiling, then there is a lowest ceiling, and this lowest ceiling is again a real number.\n",
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