I drove my High School geometry teacher crazy with this question. Since a point was defined as something with no length, width or depth I argued it could not exist. I then extended that to lines, since they were defined as an infinite array of points somehow creating length out of nothing.

I argued that if the length of a point = 0 then no number of points can create a line with length because the product of 0 and any number still = 0. Poor Mr. Priest tried to explain that it worked because the number of points between any points on a line is infinity. I responded that I had been taught that infinity times 0 still equals 0.

Of course, I extended my argument to claim I could not do my geometry homework because it required I use these non-existent, and in fact impossible constructs known as points, lines and planes. Mr. Priest eventually was compelled to abandon reason and logic to use a sheer force argument that if I did not do my homework I would fail the course.