A denumerable (or countable) set is one for which there is a correspondence from the set to N, the set of natural numbers. To put it in another way: the cardinality of the set is equal to that of the natural numbers. Every infinite subset S of the natural numbers is countable since the function that takes the least element in S to 1 and the next to least element to 2 and the next to 3 and so on, is a correspondence. This also shows that no infinite set can be "smaller" than the natural numbers. Moreover any infinite set that can be put into correspondence with a denumerable set is denumerable. Hence the integers are denumerable since the function that takes x to 2*X² + x + 1 is a correspondence from the integers to a subset of the natural numbers. Also if X and Y are denumerable sets then the set...