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  "body": "\n## Statement\n\nLet $x$ be a real number and let $n$ be an integer.\nThen $n = \\lfloor x \\rfloor$ if and only if $n \\le x \u003c n + 1$.\nIn particular, $\\lfloor x \\rfloor \\le x \u003c \\lfloor x \\rfloor + 1$.\n\n## Remarks\n\nThus the [[floor|0YVRNEDSVG]] of $x$ is the unique integer $n$ with $n \\le x \u003c n + 1$.\nThe fractional part of $x$ is $x - \\lfloor x \\rfloor$. It lies in the interval $[0, 1)$.\nAn equivalent form: $x - 1 \u003c \\lfloor x \\rfloor \\le x$.\n\n## Explanations\n\n### L1 human\n\nThe intervals $[n, n + 1)$ for integers $n$ cover the number line without overlap.\nEach real number lies in exactly one of them, and the floor of the number is the left end of that interval.\n",
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