Having mastered finite sets, we now turn to understanding the infinite. We’ve learned that \({\mathbb {N}}\) is infinite and that \({\mathbb {Q}}\) is infinite. Are they equivalent? In some sense, we can count \({\mathbb {N}}\) and it may feel as though we cannot count \({\mathbb {Q}}\) —that is, as though we cannot list a first element, second element, third element, and so on. However, we shall see that \({\mathbb {Q}}\) and \({\mathbb {N}}\) are, in fact, equivalent. Interestingly, even though we know that between any two real numbers there is a rational number, \({\mathbb {R}}\) and \({\mathbb {Q}}\) are not equivalent, as we’ll see at the end of this chapter by applying Cantor’s clever diagonal argument.