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  "body": "\n## Definition\n\nAn ordered field is a field $F$ with a total order $\\le$ on $F$.\nThe order must have these two properties for all $a$, $b$ and $c$ in $F$:\n\n1. if $a \\le b$, then $a + c \\le b + c$;\n2. if $0 \\le a$ and $0 \\le b$, then $0 \\le a b$.\n\n## Remarks\n\nIn an ordered field, each square is nonnegative: $a^2 \\ge 0$ for each $a$. In particular $1 = 1^2 \u003e 0$ and $-1 \u003c 0$.\nAn equivalent definition uses a positive cone $P$. This is a subset of $F$ that is closed under addition and multiplication.\nAlso, $F$ must be the disjoint union of $P$, $\\{0\\}$ and $-P$.\nThe field $\\mathbb{C}$ of complex numbers [[has no such order|01CJRJKDAA]].\n\n## Explanations\n\n### L1 human\n\nAn ordered field is a number system where you can add, multiply, divide and compare numbers.\nThe rules of comparison are the usual ones.\nIf you add the same number to both sides of an inequality, the inequality stays true.\nThe product of two positive numbers is positive.\n",
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