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.