Difference between revisions of "Floor function"
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Revision as of 13:13, 8 January 2018
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Research consensus and handling negative numbers
\newcommand{\Floor}[1]{ {\text{Floor}{\left({#1}\right)} } }
Definition
For x\in\mathbb{R}_{\ge 0} there is no variation on the meaning of the floor function, however for negative numbers there are varying conventions.
Non-negative
Defined as follows:
- \text{Floor}:\mathbb{R}_{\ge 0}\rightarrow\mathbb{N}_0 by \text{Floor}:x\mapsto\text{Max} (T_x) where T_x:\eq\big\{n\in\mathbb{N}_0\ \big\vert\ n\le x\big\}\subseteq\mathbb{N}_0\subseteq\mathbb{R}_{\ge 0} - note that the maximum element is defined as T_x is always finite.
- This has the property that x\le\Floor{x} .
Negative numbers
Researching this opened my eyes to a massive dispute.... consensus seems to be that x\le \Floor{x} is maintained, rounding is a separate and massive issue!
