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

You are looking for a number that, when multiplied by 0, equals 1. No real number does that, so you need to define a new system of numbers, and we want that system to be self-consistent. What other properties does this number (call it *q*) have? Can I add it to itself or another number and get another number? Does 0 × *q* equal *q* × 0? If *p* is the number that, when multiplied by 0, equals 2, what does *p* × *q* equal? Are *q* and *p* different numbers? If not, does *p* = 2*q*? It turns out it is tough to answer these questions in a satsifactory way.