On the complex plane, you can take the limit as n->0 of 1/n from any direction on the circle. The Riemann Sphere [1] ties up all these infinities into one and

On the complex plane, you can take the limit as n->0 of 1/n from any direction on the circle. The Riemann Sphere [1] ties up all these infinities into one and places it at the North Pole, opposing zero which is at the South Pole. Since now all these directional limits converge to the same value, the limit is well-defined in the Riemann Sphere and so we can close it, giving 1/0 the well-defined value of infinity. [1] https://en.wikipedia.org/wiki/Riemann_sphere https://en.wikipedia.org/wiki/Riemann_sphere