Take the curve y = 1/x from x = 1 outward, spin it around the axis, and you get a trumpet that narrows forever and never closes. Evangelista Torricelli published the shape in 1644 and showed what upset people about it: the horn holds a finite amount, exactly π if the units are kept simple, while its inside surface is infinite. So you could fill it with paint and still never manage to paint it. The way out is that filling it is painting it. Pour the paint in and it coats every bit of the wall, only the coat gets thinner the further down the horn it goes, far thinner than any brush would leave it. The paint was never short. What ran out was our idea of how thick a coat has to be before it counts.