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

They can do it, but it doesn’t really have any useful properties and you can’t do a lot with it. The main reason why mathematicians still use i for the square root of minus one is because i is useful in a lot of equations that have real world applications.

To the extent that we want or need to do math that involves dividing by zero we can use limits and calculus. This lets us analyze these equations in a logical way that yields consistent results.