User:Jshflynn/Definition:Empty word

Definition

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

Then $x$ is an empty word iff it is of length $0$.

This word is shown to be unique in Empty Word is Unique.

Hence we may speak of the empty word.

It is denoted $\lambda$ or $\epsilon$

Synonyms

Some authors call this:

• The empty string

• The null word

• The null string