Definition:Zero Digit

Definition
Let $x \in \R$ be a number.

Let $b \in \Z$ such that $b > 1$ be a number base in which $x$ is represented.

By the Basis Representation Theorem, $x$ can be expressed uniquely in the form:


 * $\displaystyle x = \sum_{j \mathop \in \Z}^m r_j b^j$

Any instance of $r_j$ being equal to $0$ is known as a zero (digit) of $n$.

Also known as
The somewhat dated term cipher or cypher can on occasion be seen for the zero digit.