Zero Padded Basis Representation

Theorem
Let $b \in \Z: b > 1$.

Let $m \in \Z_{> 0}$.

For every $n \in \Z_{> 0}, n < b^m$, there exists one and only one sequence $\sequence {r_j}_{0 \mathop \le j \mathop \le m}$ such that:


 * $(1): \quad \displaystyle n = \sum_{j \mathop = 0}^m r_j b^j$
 * $(2): \quad \displaystyle \forall j \in \closedint 0 m: r_j \in \N_b$

Comment
The sequence $\sequence {r_j}_{0 \mathop \le j \mathop \le m}$ is the
 * Definition:Number Base