Set of all rational sequences countable?

[rat bass]

I know that Q (rational numbers) are countable and that the finite cartesian of Q with itself, Q^n is countable but is it true that the countably infinite cartesian product of Q with itself is countable? The set of all rational sequences are isomorphic to Q^∞ (here I am saying Q^∞ is the countable cartesian product of Q with itself) so if I know Q^∞ is countable then I know the set of all rational sequences is countable. I need this result to prove something else for a homework problem and I want to be able to justify it.

 

[pwsnafu]

Think about the real numbers.

 

[rat bass]

ah nevermind I see it. Thank you I was wrong.