Is the set {$ 1,\frac{1}{2},\frac{1}{4},\frac{3}{4},\frac{1}{8},\frac{3}{8},\frac{5}{8},\frac{7}{8},\frac{1}{16},\frac{3}{16},....$} dense in [0,1]
How can I show that the set of rational numbers with denominator a power of two form a dense subset of the reals?