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  "body": "\n## Statement\n\nThe [[real numbers|08J2M1JYAG]] $\\mathbb{R}$, with their addition, multiplication and [[order|0337CYB0VD]] $\\le$, form an [[ordered field|010JCV9J4E]].\nThat is, $\\le$ is a total order with two properties for all real numbers $a$, $b$ and $c$.\nIf $a \\le b$, then $a + c \\le b + c$. If $0 \\le a$ and $0 \\le b$, then $0 \\le a b$.\n\n## Remarks\n\nThe ordered field $\\mathbb{R}$ contains $\\mathbb{Q}$ as an ordered subfield.\nThe order of $\\mathbb{R}$ is the only order that makes $\\mathbb{R}$ an ordered field. The nonnegative reals are exactly the squares.\n\n## Explanations\n\n### L1 human\n\nAll the usual rules for inequalities hold for the real numbers.\nFor example, from $a \\le b$ you get $a + 5 \\le b + 5$, and from $a \\ge 0$ and $b \\ge 0$ you get $a b \\ge 0$.\n",
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