Let D be the ordered set of all possible words (not just English words, all strings of letters of arbitrary length) using the Latin alphabet using only lowercase letters. The order is the lexicographic order as in a dictionary (e.g.\ aa<aaa<dog<door). Let A be the subset of D containing the words whose first letter is `a' (e.g.\ a∈A, abcd∈A). Show that A has a supremum and find what it is.