I'm having trouble understanding the construction of the Cantor Set as defined by wikipedia.
In particular, we have that
$$ C_0 = [0,1] $$
and then
$$ C_1 = [0, \frac{1}{3}] \cup [\frac{2}{3}, 1] $$
My problem is that wikipedia then states that we can view $C_n$ as the following
$$ C_{n} = \frac{C_{n-1}}{3} \cup \left(\frac{2}{3}+\frac{C_{n-1}}{3}\right) $$
so that $C = \bigcap_{n = 0}^{\infty} C_n$. But above, we have that the interval $C_{n-1}$ is being multiplied by $\frac{1}{3}$ and then in the second instance is being added onto $\frac{2}{3}$. I'm not aware of any standard method to add and multiply numbers by intervals. What is here being designated?