how would i show that the set S = {cubed root(n+1) - cubed root(m) such that n,m are in N the natural numbers} is dense in the real numbers? the book says to use the fact that (cubed root(n+1) - cubed root(n)) is less than epsilon if n is greater than n0. i'm just in an elementary proof course. could anyone show me how to prove this? i would love some help.