Prove that the set of sequence with rational terms is uncountable.

Does this mean that rational numbers are countable? do i solve this by contradiction?

There are seventy thousand ways to solve this. Try proving that the set of all \(\displaystyle f:\mathbb{N}\to\{0,1\}\) is uncountable (Cantor's Diagonalization method).

Or, note that this is equipotent to the power set of the reals.

Or, note that \(\displaystyle \aleph_0^{\aleph_0}=\mathfrak{c}\)

etc.

And no. It means that the set of all functions from the naturals to the rationals is uncountable.