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  "body": "\n## Definition\n\nLet $x$ be a real number.\nThe floor of $x$, written $\\lfloor x \\rfloor$, is the greatest [[integer|0C4JS9RF5M]] $n$ with $n \\le x$.\nThe floor function is the function $\\mathbb{R} \\to \\mathbb{Z}$, $x \\mapsto \\lfloor x \\rfloor$.\n\n## Remarks\n\nThe greatest such integer exists because the [[reals are Archimedean|0A3GWZ86AY]] and because of the [[well-ordering principle|01BX15HSRR]].\nFor each integer $n$, $\\lfloor n \\rfloor = n$. For example, $\\lfloor \\pi \\rfloor = 3$ and $\\lfloor -0.5 \\rfloor = -1$.\nThe [[characterization of the floor|0R9B0B5458]] gives an equivalent definition.\n\n## Explanations\n\n### L1 human\n\nThe floor of a number rounds it down to a whole number.\nOn the number line, it is the nearest integer at the number or to its left.\nFor negative numbers, take care: the floor of $-1.2$ is $-2$, not $-1$.\n",
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