Comparing Keys

Let ``$\le$'' be a relation on keys that induces a total ordering.

That just means that any two keys can be compared with ``less than or equal to.''

For the phone-book problem, ``less than or equal to'' refers to lexicographic ordering. For other problems, it might mean ``no shorter than'' or ``to the left of'', etc.

For current purposes, we need not assume that that keys are numbers, but it is sometimes easier to think of them that way.