PlanetMath: ceiling

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ceiling

(Definition)

The ceiling of a real number is the smallest integer greater than or equal to the number. The ceiling of 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 (), since $\lceil 3.5\rceil = 4$ and .

The notation for floor and ceiling was introduced by Iverson in 1962[1].

Bibliography

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

"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 4981 times total.

Classification:

AMS MSC:	26A09 (Real functions :: Functions of one variable :: Elementary functions)
	11-00 (Number theory :: General reference works )

Pending Errata and Addenda

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