Such a clever way of pairing gives us the confidence now to think the unthinkable and face what Galileo shied away from: a more than infinity. For if you look at all the rational numbers Q, or even at just the positive rationals—the set of all these fractions—there are obviously more of them than there are natural numbers, since between any two fractions will lie another, until what was the space from one natural to the next will be crammed to bursting with them.
