Difference between revisions of "Ceiling"
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| − | The ceiling function $\ | + | The ceiling function $\mathrm{ceil} \colon \mathbb{R} \rightarrow \mathbb{Z}$ (sometimes written $\lceil x \rceil$) is defined by |
| − | $$\lceil x \rceil = \min \{ y \in \mathbb{Z} \colon y \geq x \},$$ | + | $$\mathrm{ceil}(x) \equiv \lceil x \rceil = \min \{ y \in \mathbb{Z} \colon y \geq x \},$$ |
i.e., the smallest integer greater than or equal to $x$. | i.e., the smallest integer greater than or equal to $x$. | ||
| + | |||
| + | <div align="center"> | ||
| + | <gallery> | ||
| + | File:Celingplot.png|Graph of $\mathrm{ceil}$. | ||
| + | </gallery> | ||
| + | </div> | ||
| + | |||
| + | =Software= | ||
| + | Ceiling is implemented in the Wolfram Language as Ceiling. | ||
| + | |||
| + | {| class="wikitable" style="margin:auto" | ||
| + | |+ 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]]<br /> | ||
| + | |||
| + | [[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 $x$.
Graph of $\mathrm{ceil}$.
Software
Ceiling is implemented in the Wolfram Language as Ceiling.
| 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 |
