hi guys, let $\omega_j$ a sequence such that $$
\sum_{j=0}^{+\infty} \omega_j \le \infty
$$ and for all $k$ we have $$
\omega_k \leq \sum_{j=k+1}^{+\infty} \omega_j
$$
and assume (but you can prove it is true) that for al $x$ in a certain interval $[-A,A]$ we have
$$
x = \sum_{j=0}^{+\infty} d_j \omega_j \;\;, d_j \in \left\{-1,1\right\}
$$
my question is it true that if I pick $x,y$ in such interval with $x < y$ then there's a $j_0$ such that $d_{x,j} = d_{y,j}$ for $j < j_0$ and $d_{x,j} < d_{y,j}$ for $j = j_0$
