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].

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