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.
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.
Hint: Algebraic numbers.
Another hint: Add to each rational number an irrational number.
Take $\{q\pi \vert q \in \mathbb Q^{\times}\}$