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