Noticing the possibility of defining a metric on generated groups did not require first viewing diagrams of their Cayley graphs. This is because a word in the generators is just a finite sequence of symbols for the generators or their inverses (we omit the symbol for the group operation), and so has an obvious length visually suggested by the written form of the word, namely the number of symbols in the sequence; and then it is natural to define the distance between group members \(g\) and \(h\) to be the length of a shortest word that gets one from \(g\) to \(h\) by right multiplication, that is, \(\textrm{min}\{\textrm{length}(w): w = g^{-1}h\}\). 