Length of a word over an alphabet
= Length of a word over an alphabet
{title2=$\ell(w)$}
The <length of a word over an alphabet> is the number of symbol positions in that finite <string>, counting repetitions. Thus $\ell(abba)=4$ and $\ell(\varepsilon)=0$ for the <empty word>. <Concatenation> satisfies $\ell(uv)=\ell(u)+\ell(v)$. This differs from the <word length> of a <group> element, which minimizes over representing <words> using a chosen <generating set of a group>.