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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.

2 Answers 2

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Hint: Algebraic numbers.

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

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

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    @Jason: /facepalm/2012-11-24