Take a set of discs with radii 1/n. Their total area is finite but the sum of radii is infinite, so we can just use them to cover the X and Y axes. Yeah, this i

Take a set of discs with radii 1/n. Their total area is finite but the sum of radii is infinite, so we can just use them to cover the X and Y axes. Yeah, this is pretty similar to Gabriel's horn.