Think of numbers as points on an infinitely long line. At regularly spaced intervals along this line are the integers: 0 in the center; the positive integers 1, 2, 3, and so on to your right; and the negative integers -1, -2, -3, and so on to your left. If you divide the interval between 0 and 1 in half, you find the location of the fraction 1/2. Do it again to get 1/4, and again to get 1/8, and so on—you can divide these intervals an infinite number of times in an infinite number of ways to find an infinite number of fractions.