Show that $\mathbb{Q}-\mathbb{Z}$ is dense in $\mathbb{R}$.

Question

xapproachesinfinity · Answer

Group theory? lol!

zzr0ck3r · Answer

no, there is no measure in groups

zzr0ck3r · Answer

this could be considered set theory or real analysis or advanced calc...I am just curious.

xapproachesinfinity · Answer

eh no idea! what is Q-Z here?

zzr0ck3r · Answer

The rationals without the integers

zzr0ck3r · Answer

nm I think I might have an idea

we know the rationals are dense, so for any  nonempty interval (a,b) there is a rational r s.t. a<r<b 

case 1) if b-r <1 then there is a rational r_0 between r and b, and it cant be an integer because b-r<1

case 2) b-r>1, then a<r<r+1<b and there is a rational r_1 between r and r+1, and it cant be an integer