If zero times anything is zero, and infinity times anything is infinity, then what is zero times infinity?

Question

If zero times anything is zero, and infinity times anything is infinity, then what is zero times infinity?

In: Mathematics

Answer 1

The idea that **0 * a = 0** for all **a** is a formal axiom for certain types of numbers – that is, it is fundamentally considered to be an intrinsic property of the set of numbers under consideration, not proven but instead assumed. **Infinity** is not part of any of those sets of numbers for which **0 * a = 0 f.a. a** is considered an axiom. Infinity can be defined ambiguously, and so multiplying zero by infinity does not have a single rigorous solution.