# 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 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.

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