Difference between revisions of "Ceiling"

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The ceiling function $\lceil \cdot \rceil \colon \mathbb{R} \rightarrow \mathbb{Z}$ is defined by
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The ceiling function $\mathrm{ceil} \colon \mathbb{R} \rightarrow \mathbb{Z}$ (sometimes written $\lceil x \rceil$) is defined by
$$\lceil x \rceil = \min \{ y \in \mathbb{Z} \colon y \geq x \},$$
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$$\mathrm{ceil}(x) \equiv \lceil x \rceil = \min \{ y \in \mathbb{Z} \colon y \geq x \},$$
 
i.e., the smallest integer greater than or equal to $x$.
 
i.e., the smallest integer greater than or equal to $x$.
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<div align="center">
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<gallery>
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File:Celingplot.png|Graph of $\mathrm{ceil}$.
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</gallery>
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</div>
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=Software=
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Ceiling is implemented in the Wolfram Language as Ceiling.
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{| class="wikitable" style="margin:auto"
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|+ Software Implementations
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|-
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! Software !! Implementation !! Notes
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|-
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| Mathematica || Ceiling[x] || it begins with a capital letter and is fully spelled out with square brackets
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|-
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| Python || ceil(x) || it is lowercase with parentheses and is abbreviated
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|-
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| R || ceiling() || it is lowercase with parentheses and is fully spelled out
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|}
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=See Also=
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[[Floor]]<br />
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[[Category:SpecialFunction]]

Latest revision as of 12:44, 14 July 2023

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 $x$.

Software

Ceiling is implemented in the Wolfram Language as Ceiling.

Software Implementations
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