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  "body": "\n## Definition\n\nLet $x$ be a real number.\nThe ceiling of $x$, written $\\lceil x \\rceil$, is the least [[integer|0C4JS9RF5M]] $n$ with $x \\le n$.\nThe ceiling function is the function $\\mathbb{R} \\to \\mathbb{Z}$, $x \\mapsto \\lceil x \\rceil$.\n\n## Remarks\n\nThe ceiling and the [[floor|0YVRNEDSVG]] are related by $\\lceil x \\rceil = -\\lfloor -x \\rfloor$.\nFor each real $x$, $x \\le \\lceil x \\rceil \u003c x + 1$.\nIf $x$ is not an integer, then $\\lceil x \\rceil = \\lfloor x \\rfloor + 1$. If $x$ is an integer, then $\\lceil x \\rceil = \\lfloor x \\rfloor = x$.\n\n## Explanations\n\n### L1 human\n\nThe ceiling of a number rounds it up to a whole number.\nIf a trip needs $2.1$ buses, then you must order $\\lceil 2.1 \\rceil = 3$ buses.\n",
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