User:Jshflynn/Definition:Word length

Definition

Let $\Sigma$ be an alphabet and $x$ be a word over $\Sigma$.

Then the length of $x$ is the cardinality of $x$ when interpreted as a sequence.

It is denoted $\operatorname{len}(x)$.

Examples

Example 1

Given the alphabet $\{$ a, b, c, d $\}$ and the word $x = \langle$ b, c, c, d, d, c, a, c, a $\rangle$.

Then $\operatorname{len}(x) = 9$

Note

Some authors denote this as:

• $\operatorname{lg}(x)$

• $\vert x \vert$