TITLE: Non-end points of Cantor ternary set
QUESTION [10 upvotes]: I have studied the Cantor Ternary Set $C$ . We know that the Cantor ternary  set is uncountable. Take the set $A$ as the set of all end points of the open removed segments. That is, $A=\{0,\frac{1}{3},\frac{2 }{3},\frac{1}{9},\frac{2}{9}....\}$. Now the set $C\setminus A$ is still uncountable. So the cardinality of $C$ was entirely determined by the non-end points.
My question is: Can someone write any $5$ (at least) members of $C\setminus A$?
I know $\frac{1}{4}, \frac{3}{10} \in C\setminus A$ but I don't know about any others.
Any help will be appreciated!

REPLY [4 votes]: Any element $Z$ in the Cantor Set can be written as :
$Z= \sum_{n=1}^\infty  x_n/3^n$ where $x_n=0$ or $2$.
You can substitute any combination of $0,2$ and have your number belonging to the 
cantor set