# 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