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

The concept of “limits” as used in calculus is a more precise way of treating this. 1÷0 is neither positive nor negative infinity, BUT the limit of 1/x as x approaches 0 is +infinity from the right, and – infinity from the left.

It turns out that infinities don’t behave with the same kinds of properties as numbers in general. They are best treated in conventional math as a value you can *approach* but never *equal*.

On the other hand, when you define i, and derive all the rules of how imaginary and complex numbers behave… What logically follows is a very self consistent system of mathematical rules.