Unique représentation of number.
Number representation in some system is given below:
$x = a_0 + a_1 m_0 + a_2 m_0 m_1 + ....a_l m_0 m_1 \cdots m_l$
where $m_0,m_1,\cdots, m_l $ are positive prime numbers grater than equal to 2.
For the sake of contradiction, assume that $x = b_0 + b_1 m_0 + b_2 m_0 m_1 + ....b_l m_0 m_1 \cdots m_l$ is a different representation of $x$.
subtract the above two equations, we will get
$0=(a_0-b_0) + (a_1-b_1)m_0 + \cdots (a_l-b_l)m_0m_1...m_l$ but we know that $0=0 + 0m_0 + 0m_0m_1 + ...+0m_0m_1..m_l$
so each $a_i = b_i$ and this prove that there will be unique representation for number $x$.
Question : Is the above proof correct?