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.

Title	ceiling
Canonical name	Ceiling
Date of creation	2013-03-22 11:48:21
Last modified on	2013-03-22 11:48:21
Owner	yark (2760)
Last modified by	yark (2760)
Numerical id	17
Author	yark (2760)
Entry type	Definition
Classification	msc 26A09
Classification	msc 11-00
Synonym	ceiling function
Synonym	smallest integer function
Synonym	smallest integer greater than or equal to
Related topic	BeattysTheorem
Related topic	Floor