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

Let us suppose we make a representation for the logical “number” that we would define, which is infinity. This behavior can be seen by the smaller the divisor as it approaches zero, the larger the quotient. Until the result is a number so big it is indescribable and meaningless.

What then is the value of 2 ÷ 0? Twice as much infinity?

So what is stopping divide-by-zero being assigned any number or symbol is the land of nonsense you then enter by continuing the thought experiment.