Ceiling

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.