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

Because as the lower denominator gets smaller, the answer gets larger. Any large number you assigned the value to would be wrong, and easily proven wrong by dividing the lower denominator by any whole number.