Irrationals can be separable by finding a countable dense subset.

Question

Possible Duplicate:
Is the set of irrationals separable as a subspace of the real line?

Prove the irrationals are separable directly by finding a countable dense subset.

Answer 1

Hint: Algebraic numbers.

Another hint: Add to each rational number an irrational number.

Answer 2

Take $\{q\pi \vert q \in \mathbb Q^{\times}\}$