My teacher gave me a question and I don't know if my answer is correct (he didn't tell me :( )).
The question was : if I consider the set of all functions that eventually converges to 0, this set is dense in $l^1$ ; what happens with $l^p$ with $p>1$ and $l^{\infty}$ ?
My answer was yes, this set is dense in all spaces size if I take the sequence $(0,0...) (0,1,0...) (..., \text{any sequence} ,0...)$ this converge to that sequence.