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

√-1 is consistent with other maths rules, while 1/0 isn’t.

Just consider 1/0=?, we can rearrange to make 0x?=1. But by the definition of multiply anything multiply by 0 must be 0. So that would break multiply.

i x i = -1 works and doesn’t break anything.