What’s stopping mathematicians from defining a number for 1 ÷ 0, like what they did with √-1?

Question

What’s stopping mathematicians from defining a number for 1 ÷ 0, like what they did with √-1?

In: Mathematics

Answer 1

This has been done. Those number systems are called wheels. If you have heard of fields and rings, and wheel is kind of like those.

These number systems have positive and negative zero, so that 1/-0 = -inf.

The reason you don’t see them often is because they don’t describe reality well. For any real world calculation you need to do, you can do it without diving by 0. Because of that, these number systems are more of a curiosity for mathematicians than something you’d encounter in education.