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

A reason for doing so. The rules of mathematics can change based on what you are doing, but you still need an actual reason to do something that makes sense. If some mathematics was developed where it made sense to define this value, and it added value to the mathematics to do so, you can bet they absolutely would define it for that branch of mathematics. Even then, it doesn’t mean that this definition would carry over to things like basic arithmetic.