Let D be the ordered set of all possible words (not just English words, all strings of letters of arbitrary length) using the La
tin alphabet using only lower case letters. The order is the lexicographic order as in a dictionary (e.g. 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.
Because A is that the set of all letters from the dictionary starting with the letter 'a'. And as after set A, there'll be a group containing all the opposite words .. so there exists some x during a such every other letter during a comes before it. So it's none aside from a word starting with the letter b therefore the supremum of the set A is letter b.
