1. The problem statement, all variables and given/known data I am trying to find if 5/27 and 8/9 are in the Cantor set. 2. Relevant equations [tex]C_2=[0,1/9]\cup[2/9,3/9]\cup...\cup[8/9,1][/tex] [tex]C_3=[0,1/27]\cup[2/27,3/27]\cup[4/27,5/27]\cup...\cup[26/27,1][/tex] 3. The attempt at a solution I have: [tex]8/9=(0.22)_3[/tex] and it is an endpoint in one of the closed sets of C2, so it is in the Cantor set. I also have: [tex]5/27=(0.012)_3[/tex] It is an endpoint in C3, but doesn't the 1 in the base 3 expansion mean that it isn't part of the Cantor set?