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  "body": "\n## Statement\n\nLet $x$ and $y$ be real numbers with $x \u003c y$.\nThen there is a [[rational number|0NCJ5WXN6Z]] $q$ with $x \u003c q \u003c y$.\n\n## Remarks\n\nProof idea: choose $n$ with $1/n \u003c y - x$ by the [[Archimedean property|0WH916TJNY]]. Then some fraction $m/n$ with $m \\in \\mathbb{Z}$ lies between $x$ and $y$.\nThus between two real numbers there are infinitely many rational numbers.\nThe [[irrationals are also dense|04J6G4H78J]].\n\n## Explanations\n\n### L1 human\n\nBetween any two different real numbers, however close, there is a fraction.\nFor example, between $\\sqrt{2} = 1.41421\\dots$ and $1.4143$ lies the fraction $1.41425 = 28285/20000$.\n",
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