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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].
- 1
- N. Higham, Handbook of writing for the mathematical sciences, Society for Industrial and Applied Mathematics, 1998.
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"ceiling" is owned by yark. [ full author list (2) | owner history (2) ]
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See Also: Beatty's theorem, floor
| Other names: |
ceiling function, smallest integer function, smallest integer greater than or equal to |
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Cross-references: floor, integer part, function, number, real number
There are 10 references to this entry.
This is version 12 of ceiling, born on 2001-10-18, modified 2007-05-30.
Object id is 346, canonical name is Ceiling.
Accessed 6507 times total.
Classification:
| AMS MSC: | 26A09 (Real functions :: Functions of one variable :: Elementary functions) | | | 11-00 (Number theory :: General reference works ) |
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Pending Errata and Addenda
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