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  "body": "\n## Statement\n\nThe [[real numbers|08J2M1JYAG]] $\\mathbb{R}$, with their addition and multiplication, form a field.\nThat is, $\\mathbb{R}$ is a commutative ring with $0 \\neq 1$, and each real number $x \\neq 0$ has a multiplicative inverse $x^{-1}$ with $x \\cdot x^{-1} = 1$.\n\n## Remarks\n\nThe field $\\mathbb{R}$ contains the field $\\mathbb{Q}$ of rational numbers as a subfield.\nIn the axiomatic approach, this is part of the axioms. In a construction of $\\mathbb{R}$, for example with [[Cauchy sequences|0D8HE681SC]], it is a theorem.\n\n## Explanations\n\n### L1 human\n\nThe usual rules of arithmetic hold for the real numbers.\nYou can add, subtract and multiply real numbers, and you can divide by each real number that is not zero.\n",
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