Each of these sequences be the center of a small ball, say, of radius 1/3. these balls do not intersect and we have uncountably many of them. If M is any dense set in , each of these nonintersecting balls must contain an element of M. Hence M cannot be countable. Since M was an arbitrary dense set, this shows that I cannot have dense subsets which are countable. Consequently, I is not separable.
Prove that the space L^p" with 1≤p<+infinity is separable.