2. Prove or disprove: for any real number x there is a unique map $a: \mathbb{Z} \to \{-1, 0, 1\}$ such that
$x = \sum_{n \in \mathbb{Z}} a_n 3^n$,
for any $m \in \mathbb{Z}$ there is $n \le m$ such that $a_n \ne -1$, and there is $m \in \mathbb{Z}$ such that for any $n \ge m$ we have
$a_n = 0$.
