TITLE: How to prove that the set of rational numbers are countable?
QUESTION [15 upvotes]: Can any one tell me how to prove that the set of rational numbers are countable? Prove give me a prove?
Thanks.

REPLY [4 votes]: For an explicit enumeration of positive rationals, you can use the Calkin-Wilf sequence: $$q_{i+1}= \frac{1}{ \lfloor q_i \rfloor +1 - \{q_i\} }, \ q_0=1.$$
More details can be found in Proofs from THE BOOK.