- #1

- 60

- 0

## Homework Statement

[tex]G=\{x\in R|0\leq x<1\}[/tex] and for some [tex]x,y\in G[/tex] define [tex]x*y=\{x+y\}=x+y-\lfloor x+y \rfloor[/tex]

## Homework Equations

## The Attempt at a Solution

I want to proof Associative property:

[tex]x*(y*z)=(x*y)*z \Leftrightarrow x*(y+z-\lfloor y+z \rfloor)=(x+y-\lfloor x+y \rfloor)*z [/tex]

[tex]\Leftrightarrow x+y+z-\lfloor y+z \rfloor-\lfloor {x+y+z-\lfloor y+z \rfloor}\rfloor=x+y+z-\lfloor x+y \rfloor-\lfloor x+y+z-\lfloor x+y \rfloor\rfloor[/tex]

[tex] \Leftrightarrow\lfloor y+z \rfloor+\lfloor {x+y+z-\lfloor y+z \rfloor}\rfloor=\lfloor x+y \rfloor+\lfloor x+y+z-\lfloor x+y \rfloor\rfloor[/tex]

What now?