Difference between revisions of "Floor"
From specialfunctionswiki
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| − | The floor function $\mathrm{floor} \colon \mathbb{R} \rightarrow \mathbb{Z}$ is defined by | + | The floor function $\mathrm{floor} \colon \mathbb{R} \rightarrow \mathbb{Z}$ (sometimes written as $\lfloor x \rfloor$) is defined by |
| − | $$\lfloor x \rfloor = \max \left\{y \in \mathbb{Z} \colon y \leq x \right\},$$ | + | $$\mathrm{floor}(x) \equiv \lfloor x \rfloor = \max \left\{y \in \mathbb{Z} \colon y \leq x \right\},$$ |
| − | i.e., it is the largest [[integer]] less than or equal to $x | + | i.e., it is the largest [[integer]] less than or equal to $x$. |
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Latest revision as of 00:41, 23 December 2016
The floor function $\mathrm{floor} \colon \mathbb{R} \rightarrow \mathbb{Z}$ (sometimes written as $\lfloor x \rfloor$) is defined by $$\mathrm{floor}(x) \equiv \lfloor x \rfloor = \max \left\{y \in \mathbb{Z} \colon y \leq x \right\},$$ i.e., it is the largest integer less than or equal to $x$.
Graph of $\mathrm{floor}$.
