"Sets can have an infinite number of members. That doesn’t make sense for the Davies family example, but for other things it does, of course, like: I = { k : k is a multiple of 3 } . Obviously there are infinitely many multiples of 3, and so I has an unlimited number of members. Not surprisingly, we call I an infinite set . More surprisingly, it turns out that there are different sizes of infinite sets, and hence different kinds of infinity. For instance, even though there are infinitely many whole numbers, and also infinitely many real (decimal) numbers, there are nevertheless more real numbers than whole numbers. This is the thing that drove Cantor insane, so we won’t discuss it more here. For now, just realize that every set is either finite or infinite."