# Density of a specific set

1. Oct 11, 2010

### D.K.

Is there an easy way to prove that for any irrational $$\xi$$ the set:

$$\{x \in \mathbb{R}: x = p + q\xi, \ p, q \in \mathbb{Z}\}$$ is dense in $$\mathbb{R}$$?

I know a proof involving notions from measure theory of which I unfortunately know nothing about. Any help would be very appreciated.

Last edited: Oct 11, 2010
2. Oct 11, 2010

### D.K.

Nevermind, it turned out to be rather easy.