Definition:Basis Representation

Definition
Let $b \in \Z$ be an integer such that $b > 1$.

Let $n \in \Z$ be an integer such that $n \ne 0$.

The representation of $n$ to the base $b$ is the unique string of digits:


 * $\pm \sqbrk {r_m r_{m - 1} \ldots r_2 r_1 r_0}_b$

where $\pm$ is:


 * the negative sign $-$ $n < 0$


 * the positive sign $+$ (or omitted) $n > 0$

If $n = 0$, then $n$ is represented simply as $0$.

Also known as
Informally, we can say $n$ is (written) in base $b$ or to base $b$.

Also see

 * Definition:Number Base


 * Basis Representation Theorem which demonstrates that a basis representation exists and is unique for all $n \in \Z$ and $b \in \Z_{> 1}$.


 * Definition:Basis Expansion, for real numbers which are not integers