Ceiling

https://arbital.com/p/mathematics_ceiling

by Nate Soares May 27 2016 updated May 27 2016

The ceiling of a real number $x,$ denoted $\lceil x \rceil$ or sometimes $\operatorname{ceil}(x),$ is the first Integer $n \ge x.$ For example, $\lceil 3.72 \rceil = 4, \lceil 4 \rceil = 4,$ and $\lceil -3.72 \rceil = -3.$ In other words, the ceiling function rounds its input up to the nearest integer.

For the function that rounds its input down to the nearest integer, see [floor]. Ceiling and floor are not to be confused with [fix_towards_zero fix] and [ceilfix], which round towards and away from zero (respectively).

Formally, ceiling is a function of type $\mathbb R \to \mathbb Z.$ The ceiling function can also be defined on complex numbers.

The ceiling of a real number $x,$ denoted $\\lceil x \\rceil$ or sometimes $\\operatorname{ceil}(x),$ is the first integer $n \\ge x.$ For example, $\\lceil 3.72 \\rceil \= 4, \\lceil 4 \\rceil \= 4,$ and $\\lceil -3.72 \\rceil \= -3.$ In other words, the ceiling function rounds its input up to the nearest integer\.