ABSTRACT
The terms denumerable and countable may appear to be associated with a type of finiteness, however, as you have no doubt discovered by now, mathematical terms must be defined carefully. Such is the case with these words. In particular, countable does not necessarily mean the capacity to be physically counted and denumerable doesn't even refer to finite sets. Let's find out exactly what these terms do mean. Recall that the relation = is an equivalence relation (see Exercise 23.2).
