User:Jshflynn/Definition:Word

Definition

Let $\Sigma$ be an alphabet.

Then a finite sequence in $\Sigma$ is referred to as a word over $\Sigma$.

Examples

Example 1

Given the alphabet $\{$5, a, 7, t$\}$.

Then $\langle$ a, 7, 7, 5 $\rangle$ is a word over it.

If there is no confusion then this would simply be written as 'a775'.

Example 2

Given the alphabet $\{$l, ll, lll$\}$.

Then $\langle$ l, lll, l $\rangle$ is a word over it.

In this case there would be confusion as to what sequence it represents so it is not written in the above shorter way.