Question

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

Answer 1

Group theory? lol!

Answer 2

no, there is no measure in groups

Answer 3

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

Answer 4

eh no idea! what is Q-Z here?

Answer 5

The rationals without the integers

Answer 6

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