ceiling

The 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[1].

References

1 N. Higham, Handbook of writing for the mathematical sciences, Society for Industrial and Applied Mathematics, 1998.

单词	Ceiling
释义	ceiling The 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[1]. References 1 N. Higham, Handbook of writing for the mathematical sciences, Society for Industrial and Applied Mathematics, 1998.
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