- Thread starter
- #1

- Thread starter Walshy
- Start date

- Thread starter
- #1

- Thread starter
- #3

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

- Admin
- #4

- Jul 22, 2012

- 35

$ \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

- 2,573