Ceiling

The ceiling function $\mathrm{ceil} \colon \mathbb{R} \rightarrow \mathbb{Z}$ (sometimes written $\lceil x \rceil$) is defined by $$\mathrm{ceil}(x) \equiv \lceil x \rceil = \min \{ y \in \mathbb{Z} \colon y \geq x \},$$ i.e., the smallest integer greater than or equal to $x$.

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  Graph of $\mathrm{ceil}$.

Software

Ceiling is implemented in the Wolfram Language as Ceiling.

Caption text

Software	Implementation	Notes
Mathematica	Ceiling[x]	it begins with a capital letter and is fully spelled out with square brackets
Python	ceil(x)	it is lowercase with parentheses and is abbreviated
R	ceiling()	it is lowercase with parentheses and is fully spelled out

See Also

Floor