This one is related to the Cantor set, more explicitly, how to obtain a closed formula for the Cantor set?
$$ \mathcal{C} = \bigcap_{n=1}^{\infty} \bigcap_{k=0}^{3^{n-1}-1} \left(\left[0\,,\, \frac{3k+1}{3^n}\right] \cup \left[\frac{3k+2}{3^n}\,,\,1\right] \right)$$
Equivalently, this set can also be represented as:
$$ \mathcal{C} = [0,1] \setminus \bigcup_{n=1}^{\infty} \bigcup_{k=0}^{3^{n-1}-1} \left( \frac{3k+1}{3^n} ,\frac{3k+2}{3^n}\right)$$
How do you obtain both of these formulation?
Both these formulations are mentioned in the wikipage of cantor set.