One of my correspondents revived the points in a line paradox as follows. He suggested that a countable set of points can fill a space of arbitrary size:
"The Points in a Line Paradox" (0 times infinity can be any number you choose) can be represented (conceptually anyway) in the physical world. Imagine a bucket of sand in which the sand particles are all cubes so that there is no space in between. Then imagine cutting each particle in half, doubling the number of particles. Continue this until the particles approach zero size and infinite in number. The size of the bucket will not change. The bucket can be any size to start. This shows the concept of limit also. So even a countable infinity of zeros can be any size."
Solution