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- Thread starter Walshy
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I'm sorry that makes no sense to me.floor(x) = x - a, where 0 <= a < 1

floor(-x) = -x - b, where 0 <= b < 1

You tell me why a + b = 1

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- Jul 22, 2012

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$ \begin{aligned} \lfloor{x}\rfloor+\lfloor{-x}\rfloor & = \max\{m\in\mathbb{Z}\mid m < x\}+\max\{m\in\mathbb{Z}\mid m < -x\} \\& = \max\{m\in\mathbb{Z}\mid 2m < 0\} = \max\{m\in\mathbb{Z}\mid m < 0\} \\& = -1.\end{aligned}$

This addition (of sets usually) is called Minkowski addition.

- Jan 30, 2012

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