# 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.

The word nought can commonly be seen.

## Linguistic Note

The word cipher can also be found in its less common spelling: cypher.

The word ultimately derives from the Arabic صِفْر‎ (ṣifr), meaning zero or empty.