Definition:Zero Digit

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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.