Let $b \in \mathbb{Z}: b>1 .$ For every $n \in \mathbb{Z}^{+}$, there exists one and only one sequence $\left\langle r_{j}\right\rangle_{0 \leq j \leq t}$ such that: 1. $\quad n=\sum_{k=0}^{t} r_{k} b^{k}$ 2. $\quad \forall k \in[0 \ldots t]: r_{k} \in \mathbb{N}_{b}$ 3. $\quad r_{t} \neq 0$ This unique sequence is called the representation of $n$ to the base $b$, or, informally, we can say $n$ is (written) in base $b$