We have $D = \bigcup_{n \in \mathbb{N}^{\star}} D_n$ where $D_n = \left\{\sum_{j=1}^{n} \frac{x_j}{2^j}, (x_j)_{j \in \llbracket 1,n \rrbracket} \in \{0,1\}^n\right\}$. Is the set $D$ countable?
We have $D = \bigcup_{n \in \mathbb{N}^{\star}} D_n$ where $D_n = \left\{\sum_{j=1}^{n} \frac{x_j}{2^j}, (x_j)_{j \in \llbracket 1,n \rrbracket} \in \{0,1\}^n\right\}$.
Is the set $D$ countable?