Difference between revisions of "Ceiling"
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The ceiling function $\mathrm{ceil} \colon \mathbb{R} \rightarrow \mathbb{Z}$ (sometimes written $\lceil x \rceil$) is defined by | The ceiling function $\mathrm{ceil} \colon \mathbb{R} \rightarrow \mathbb{Z}$ (sometimes written $\lceil x \rceil$) is defined by | ||
| − | $$\mathrm{ceil}(x) = \min \{ y \in \mathbb{Z} \colon y \geq x \},$$ | + | $$\mathrm{ceil}(x) \equiv \lceil x \rceil = \min \{ y \in \mathbb{Z} \colon y \geq x \},$$ |
i.e., the smallest integer greater than or equal to $x$. | i.e., the smallest integer greater than or equal to $x$. | ||
Revision as of 00:42, 23 December 2016
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 $\mathrm{ceil}$.
