Now we can return to Galileo’s shorter and longer line-segments. The open interval (0, 1) has more points on it than all the counting numbers in the world, although there is no end of them. What about the longer segment (0, 2)? An astonishingly simple proof—another “Look!”—shows that this longer segment contains just as many points as the first: there is a 1–1 correspondence between them.
