How is it possible to divide by zero in the Reimann’s sphere? In other words how come there is no such thing as a negative infinity?

Question

I recently did some (really short) research on dividing by zero and heard it is possible to divide by zero in the Riemann’s sphere, because it only defines a positive infinity and not a negative one. Is that true? And how does that work? Can’t we always find a negative of a certain number?

In: Mathematics

Answer 1

Riemann’s sphere pretty much introduces a wrap-around at infinity, so infinity is like zero in terms of not having a sign, being its own negative (well, except for the fact that adding two of them gets you infinity instead of zero) and so on. Poles are no longer undefined and are in fact not even discontinuities anymore.