ceilingCeiling2001-10-18 23:28:542007-05-30 05:51:47Definition\usepackage{amssymb}
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The \emph{ceiling} of a real number is the smallest integer greater than or equal to the number. The ceiling of $x$ is usually denoted by $\lceil x\rceil$.
Some examples:
$\lceil 6.2\rceil=7$, $\lceil 0.4\rceil=1$, $\lceil 7\rceil=7$, $\lceil -5.1\rceil=-5$, $\lceil \pi\rceil=4$, $\lceil -4\rceil=-4$.
Note that this function is not the integer part ($[x]$), since
$\lceil 3.5\rceil = 4$ and $[3.5]=3$.
The notation for floor and ceiling was introduced by Iverson in 1962\cite{Higham}.
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\bibitem{Higham} N. Higham, Handbook of writing for the mathematical sciences, Society for Industrial and Applied Mathematics, 1998.
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