 Cantor’s arithmetization of the continuum had the following important consequence. It had long been recognized that the sets of points of any pair of line segments, even if one of them is infinite in length, can be placed in one-one correspondence. This fact was taken to show that such sets of points have no well-defined “size”. But Cantor’s identification of the set of points on a linear continuum with a domain of numbers enabled the sizes of point sets to be compared in a definite way, using the well-grounded idea of one-one correspondence between sets of numbers.