The basic problem of enumerative combinatorics is that of counting the number of elements of a finite set. Usually are given an infinite class of finite sets S i where i ranges over some index set I (such as the nonnegative integers ℕ), and we wish to count the number ƒ(i) of elements of each S i “simultaneously.” Immediate philosophical difficulties arise. What does it mean to “count” the number of elements of S i ? There is no definitive answer to this question. Only through experience does one develop an idea of what is meant by a “determination” of a counting function ƒ(i).