Why is the set of Rational numbers ,$\mathbb Q$, a countably finite set?  I think that - if we assign $n$ to a rational number, and $n+1$ to another rational number, Then I can surely find a rational number in between these two, which is not accounted for.  I using the definition - If a set is countably infinite, then each element of the set can be mapped to the set of natural numbers.  Another question - Is the cardinal product of countably infinite set of countably infinite sets uncountable or countable?
Can any one tell me how to prove that the set of rational numbers are countable? Prove give me a prove?  Thanks.
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